The vote will be held in the district of Hougang, whose opposition member of parliament Yaw Shin Leong was expelled by the Workers' Party due to charges of personal misconduct, creating a vacancy in the 87-member legislature.
Analysts said the vote will be a fresh test for the ruling People's Action Party, one year after a landmark general election in which its share of the national vote fell to an all-time low of 60 percent.
It has been in power since 1959 but criticism of the government over rising living costs, a large influx of foreigners and frequent breakdowns in the metro train system has intensified on the Internet even after last year's election.
Online forums and social media now shape political debate in Singapore, a traditionally tightly ruled country of 5.2 million people where the mainstream media have long been identified with the government.
In last year's vote, the Workers' Party won an unprecedented six seats despite an electoral system seen as stacked in favour of the ruling party.
Reuben Wong, an assistant professor of political science at the National University of Singapore, believed the opposition will retain Hougang but with a narrower margin because of the impact of allegations of extramarital affairs by Yaw, who has remained silent.
"Hougang has been a Workers' Party stronghold for so many years, it's very difficult to wrest control from Workers' Party," Wong told AFP.
Prime Minister Lee Hsien Loong, in a statement after the by-election was called, criticised the opposition party and Yaw for failing to give a full account of the allegations as well as his expulsion.
"Both the WP and Mr Yaw have let down all those who voted for him," Lee said.