The newest findings from YouGov put support for separation at 44 per cent - one point lower than the independence referendum in 2014.
Backing for the union is at 56 per cent.
The survey also suggests only 31 per cent of Scots want the Scottish Government to campaign for independence in the next two years.
Of those who voted yes in 2014, only 60 per cent would be happy if the SNP campaigned for independence in that timescale.
Polster John Curtis said the survey was the first to suggest the yes vote had fallen since the indy ref.
A spokesman for the Scottish Conservatives said: “The standout finding from this poll is the increasing opposition to another referendum on independence, and the drop in support for independence itself now lower than at anytime since the 2014 referendum.
“On the day the SNP finish their so-called listening exercise on independence, it is now time they finally paid attention to what Scotland it saying - no to a second referendum and no to more division , more uncertainty and more rancour.”
A Scottish Labour spokesman added: “This poll is further evidence that a growing number of Scots are opposed to the SNP’s latest attemot to divide our country.”
The survey also put support for SNP in a constituency vote at 48 per cent and 39 per cent in a regional vote.
The SNP, which completed gathering information for its national survey on independence today, said: “This poll shows continued strong support for the SNP, with nearly 50 per cent backing in an election for Scottish parliament constituencies, nine years into government. That is a very powerful endorsement of the party#s time in office and of Sturgeon as First Minister.”