A revised electoral code bars candidates who supported the ex-president's bid to change the constitution, though Compaore's party could have a strong showing in the legislative election.
Some 5.5 million people are registered to vote, according to the election commission, which has said it will publish preliminary results as soon as Monday.
A candidate needs more than 50 percent of the vote to avoid a run-off, which would be held 15 days after first-round results are finalised.
More than 17,000 local and foreign observers are expected to monitor the poll. Security Minister Alain Zagre has said 25,000 soldiers and police will be deployed across the country.
Source: Agencies