The International Foundation for Electoral Studies says it is the first time, since its surveys began last December, that she is not the first choice.
The survey, conducted between March 21 and 28, shows 19 per cent support for Golkar compared to 8.6 per cent for PDI-P and 7.3 percent for the National Mandate Party, led by national assembly speaker Amien Rais.
However, more than half the respondents declined to say who they will vote for or had yet to make up their minds.
For the presidential election on July 5, Mr Yudhoyono has 18.4 per cent support compared to 11.6 percent for Mrs Megawati.
Mr Yudhoyono quit his ministerial post last month after complaining that the president was freezing him out of cabinet meetings because of his presidential bid.
A separate poll by the Indonesian Survey Institute, conducted on March 18, a week after the campaign began, shows 23.2 per cent for Golkar and 17.5 percent for PDI-P.
When asked about presidential preferences, almost 21 per cent picked Mr Yudhoyono, 17.4 per cent chose Mrs Megawati.
More than 147 million people in the world's third largest democracy are eligible to vote.
Just some background figures...