The Awaz FM poll showed 64% of listeners would vote Yes, while 32% were against the idea of breaking up the United Kingdom.
It comes as grass-roots campaigning on the issue is being stepped up in the Scottish Asian community, with both the Yes and No camps planning to put their case through street stalls, leafleting and a presence at multicultural festivals.
Next month a debate on independence aimed mainly at young Muslims, which will include a mock referendum vote, will also be held at the University of Strathclyde.
The event on March 9 is being organised by the Federation of Student Islamic Societies (FOSIS), with the panel of speakers including Scottish Labour deputy leader Anas Sarwar and the SNP's external affairs minister Humza Yousaf.
Organiser Anum Qaisar, student affairs representative for FOSIS Scotland, said: "It will be aimed at young Muslims, but it is going to be opened up to everyone as I do think it is such an important issue.
"I may be Muslim and I may have a Muslim background but I identify myself as a Scottish person and a member of the United Kingdom, and I think this is a very important decision that everyone does need to make an informed choice on."
Qaisar said she felt opinions among the Muslim community were currently split on the issue, but she would be voting against independence. She said: "For me, it is the basic concept that I think countries should be building bridges and not borders."
Many Asian women are making sure their voices are heard in the debate, including lawyer Tasmina Ahmed-Sheikh, an advisory board member for Yes Scotland and a representative for the group Scots Asians For Yes. She said she believed the independence vote was helping to engage women - particularly older members of the community - in politics.
"What we term as 'Aunty-jis' are engaging in the referendum, they are interested in what it means for them, their families and their future and they think it matters," she said. "We are now third, fourth-generation Asian - we don't consider ourselves Asians living in Scotland, we consider ourselves Scottish Asians."
Ahmed-Sheikh said factors such as the "extreme right-wing rhetoric" from south of the Border were influencing attitudes towards independence.
She pointed to the example of a Home Office poster campaign last year which was branded xenophobic for telling people not eligible to stay in the UK to ask about "going home".
"These things have upset people and I don't think it is reflective of the type of Scotland in which we live at all," Ahmed-Sheikh said.
In the mid-2000s, it was reported that many Muslim voters who traditionally supported Labour had switched to the SNP as a protest against war in Iraq.
Dr Timothy Peace, a postdoctoral fellow at Edinburgh University who specialises in research into British Muslims and political participation, said previous election results indicated Labour was still the party backed by most Muslims in the UK. But he added: "You could be a firm Labour voter but still think that independence is in your interests.
"There is no doubt that Muslims in Scotland feel Scottish, but that doesn't necessarily mean they want to vote for an independent Scotland. The feeling I get from speaking to people is people are divided on the issue and there is certainly a lot of votes still up for grabs."
Human rights lawyer Aamer Anwar, a member of the Scots Asians For Yes campaign, said politicians and community leaders could no longer rely on garnering a block vote.
"When you talk about a block vote, they will literally go door-to-door when it comes to election times and expect families to deliver sometimes 400-500 votes at a time," he said.
"That is the way it is done on the Asian sub-continent and the process was carried back to Scotland.
"I think for the second or the third or sometimes the fourth generation, people have had enough of having a vote taken for granted.
"Some of the community leaders who were the first here in the 50s, 60s and 70s, and who fought for the community, did a very admirable job. But times have moved on and it is no longer the case that they demand a vote and it has to be instantly delivered."
Anwar said he believed the independence referendum was about "changing the destiny of our children".
"That for me sums up the decision that I make come September, and the rest of Scotland will make," he said. "It will have an impact on my children and my children's children."
Blogger and community campaigner Talat Yaqoob, a supporter of the Better Together campaign, said she would be voting No because she believed there were political and economic benefits to remaining as part of the UK.
She added: "One of the aspects that is most important to me in this referendum is ensuring a diverse set of voices is being heard and Scotland is truly represented at the polls."
A spokesman for Awaz FM said those who participated in the survey were likely to be younger listeners, but cautioned that, like other web polls, it was not "truly indicative".
He added that they planned to repeat the poll in the run-up to the referendum vote.