Tayside Police told staff in an email to look at "alternative disposals", including issuing warnings and tickets, while Strathclyde Police confirmed it had issued a similar instruction.
It came ahead of yesterday's protest action by solicitors in Glasgow, Edinburgh and Paisley.
The move resulted in them refusing to represent accused people appearing from custody who had been arrested over the bank holiday weekend. The lawyers are angry at plans by the Government to make controversial changes to criminal legal aid.
Chief Inspector Conrad Trickett of Tayside Police emailed colleagues informing them it was possible lawyers would strike at some point this week as the courts would have been closed on Monday because of a day off for St Andrew's Day.
He wrote: "The Perth and Dundee Bar Association have voted to support the industrial action by solicitors.
"PF [procurator fiscal] Helen Nisbet has no information about when the action may take place.
"While officers should not be deterred from arresting offenders where necessary, full consideration should be given to use of discretion and other available disposals to try to minimise the impact on custody arrangements and those of our criminal justice partners, which will already be stretched after a holiday weekend."
Strathclyde Police confirmed the force had advised officers to consider alternatives to arresting people but claimed the instruction was not unique to the dispute.
At Glasgow Sheriff Court it was said the number of people going through the custody court yesterday was significantly lower than expected following a Monday holiday for court staff, with just 131 accused. It compared to 125 on Monday the previous week. In Paisley, 31 people went through custody yesterday, compared to 25 the previous Monday.
Scottish Conservative Chief Whip John Lamont said: "It is almost unbelievable that police officers in two of Scotland's major cities should go into their shift with this message ringing in their ears. It also means for an entire weekend alleged criminals who would normally be arrested and brought to justice have clearly been getting an easy ride."
Labour's Lewis Macdonald added: "If offenders in Tayside and Strathclyde are walking free when they would normally have been detained, that outcome clearly arises from Kenny MacAskill's failure to hold meaningful discussions with lawyers to end the current industrial action in our courts."
The solicitors are taking action over Mr MacAskill's plans to force anyone with a disposable income of £68 or above to pay a contribution towards their legal fees.
They claim it would undermine the rights of accused people to have the best defence regardless of cost.
The SNP wants lawyers to collect the contributions from their sum-mary clients in a move that could save £3.9 million, but lawyers claim that the Scottish Legal Aid Board should collect the money. Most accused represented themselves yesterday, causing delays. Ann Ritchie of the Glasgow Bar Association said it reflected "how it will be if the Government's proposals go ahead. It's not in the interests of justice".
She added: "This is not a decision solicitors have taken lightly, it goes against everything we believe in, to leave clients to fend for themselves, but we feel we have to make a stand."
Cameron Tait, of the Edinburgh Bar Association, added: "The profession struggles to understand why the Government is intent on driving through badly thought out changes in the face of concerns not just from solicitors but academics and charities."
A Government spokesman said it was deeply concerning that accused people were appearing in court unrepresented. He added the Government was hoping to continue its dialogue with those involved in the dispute.
A spokesman for Tayside Police said the email specifically advised its officers "not to be deterred from arresting offenders where necessary". He added: "That could not have been clearer."
A Strathclyde Police spokeswoman added: "We regularly remind officers as to the Lord Advocate's guidelines and other options at their disposal."