Michael Matheson insisted the Scottish Government was still "unconvinced" about making such a change.
He spoke out as Holyrood debated a petition backed by more than 20,000 people calling on ministers to introduce an opt-out system for organ donation.
Wales is introducing an new system of deemed consent at the end of next year, where organs can be taken for transplant unless people have made it clear they do not wish this to happen after their death.
Mr Matheson told MSPs the Scottish Government would monitor the situation in Wales to see what impact the change had.
But he stated: "It would be fair to say we remain unconvinced that we should make any move to introduce an opt-out system right now.
"I want to make sure that we keep this issue under review and learn from what happens in Wales, but we are making great progress here in Scotland with the programme of activity we have under way."
The minister added: "People believe opt-out will mean more organs will become available but our own experts tell us this is not necessarily the case.
"Opt-out means increasing the proportion of the population on the organ donor register but you don't need to be on the organ donor register to be a donor. Over the last five years, 62% of all donors in Scotland are not on the donor register.
"The real issue that limits the number of donors is the number of people who die in circumstances where donation is possible.
"Unfortunately, to become an organ donor you really have to die in intensive care, and only about 1% of deaths in Scotland occur in these circumstances. Sadly that's something opt-out in itself can not change."
Mr Matheson said the US had a higher organ donation rate than Scotland but did not have an opt-out system while Sweden has an opt-out system, but has a lower donation rate than Scotland.
"There is no single thing that will bring about the revolution in donation rates," Mr Matheson said.
He stressed the Scottish Government was "committed to increasing organ donations in Scotland", adding: "I don't believe any other country in the UK can say it has done more on this agenda in the last five years than what has happened here in Scotland."
He told how Scotland had almost doubled the number of organ donors in the last six years, adding there had been a 62% rise in transplants being carried out - the highest increase in the UK.
Meanwhile, there has been a 25% reduction in the transplant waiting list since 2006-07, Mr Matheson said.
He told MSPs: "We're making the best progress in the UK. We're seeing more donors and we're delivering more transplants and we're saving more lives as a result.
"We will keep on review how the opt-out process progresses in Wales, but while we are making the sort of progress we have delivering here in Scotland over recent years, I believe it is prudent and appropriate that we should wait to see what happens in Wales before we start to introduce significant legislative change here in Scotland."
Labour accused ministers of "pulling back" from a possible move to an opt-out system for organ donation.
Rhoda Grant said: "Previously the Scottish Government had indicated support for a soft opt-out system, but today they appear to be pulling back from that, and that's really disappointing.
"If they wait for an evaluation of the changes in Wales it will be well into the next decade before we see that change happening in Scotland, and that will be too late for pretty much everyone who is already waiting.
"We need to make a step change now."
The Labour MSP said: "There are around 600 people in Scotland waiting for an organ transplant. Sadly, some of them will die before being offered a transplant.
"But we could come closer to meeting that need if everyone who could donate did donate."
She argued the current system, where families have to give consent for their loved one's organs to be taken for transplantation, meant people had to make a decision on this "at the most harrowing time of their lives".
Ms Grant said the system to be introduced in Wales at the end of 2015 would see people asked to confirm their relative's wishes.
If people have either opted out of the organ donor register, or have told their family their organs are not to be used, no transplant should take place.
"This system has the ability to increase donation," Ms Grant said.
"Ninety per cent of people agree with donation yet only 41% of Scots are registered on the organ donation register."
But she said in Scotland families were asked to make a decision on the issue "at a time of great distress when it is almost impossible for them to think straight".
The Labour MSP added: "Given that only 10% object to donation, it is surely best to ask them to register that objection, this way every potential donor can have their own wishes prevail."
Tory health spokesman Jackson Carlaw backed the Government's stance.
While he said there was a "fully worked through" opt-out system being implemented in Wales from December 2015, he added: "We do not yet know whether that fully worked through legislative solution will prove to be wholly robust or wholly effective.
"It does seem to me that the minister's assessment is to remain sympathetic to what is being done and to wait and see and watch carefully and use that then if it is successful as a template for legislation in this Parliament."