The vote for 15 seats in the upper house of parliament has been postponed twice already as the epidemic has swept the impoverished nation, killing 3,290 people.
Balloting began at 7:30 am (local time) and is due to end at 5:00 pm.
Football star George Weah - who played for Chelsea and AC Milan before retiring from the game in 2003 - and the son of President Ellen Johnson Sirleaf, Robert Sirleaf, are among the 139 candidates in the running for a seat.
Liberia was the country worst hit by the deadly virus until it was overtaken by a recent surge in new infections in neighbouring Sierra Leone.
Liberia's Deputy Health Minister Tolbert Nyensuah said all the voters would be tested and those with high temperatures would be asked to cast their ballots in a separate area.
Joey Kennedy, a spokesman for the national election commission, had earlier said that all voters would have to wash their hands before entering polling stations and maintain at least a metre's distance from each other.