Michael Matheson insisted the Scottish Government was "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 a new system of deemed consent, 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 we should make any move to introduce an opt-out system right now. 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.
"The real issue that limits the number of donors is the number of people who die in circumstances where donation is possible."