Interior Minister Elias Murr said less than 50,000 of 250,000 registered voters took part in the Baabda-Aley district election, east of Beirut.
"The only explanation for the low turnout is that people may have become tired of political conflicts in the country. Their only problem has become their daily bread," he said at a press conference after polling closed.
Aounist candidate Hikmat Dib ran in the election to replace former minister and MP Pierre Helou, who died in August from a brain haemorrhage after collapsing during a live television show.
It is the first time that a supporter of Aoun - the former leader ousted in 1990 in a Syrian-led offensive - has stood for election for the Free National Current (FNC), which has always refused to recognise the Syrian-backed government in Lebanon.
Dib, an engineer and an FNC activist, was jailed during a crackdown in August 2001 that saw 200 activists opposed to Syria's military presence and political dominance in Lebanon imprisoned.
Henry Helou, son of the deceased politician and backed by the influential government Druze MP Walid Jumblatt, is also standing for the Maronite seat.
Relations between the two candidates are very poor. The FNC questions how Jumblatt became a deputy previously, while Jumblatt condemns FNC calls for an immediate end to Damascus-backed power in Lebanon.
Some 250,000 electors are eligible to vote in the by-election. Half are Christians, the rest are Druze and Shia Muslims.