His detention on March 13 came as opposition leaders prepared for a mass rally on March 25.
Vyachorka's son, Franek, said police detained his father as he returned home Tuesday night and that he did not know his whereabouts.
Vyachorka is the chairman of the Belarusian Popular Front, the country's largest opposition party.
Also on the night of March 13, police in Minsk detained another opposition figure, Vyachaslau Siuchyk, a member of the Christian Conservative Party.
The detentions came amid a campaign by police to interrogate opposition youth ahead of a rally on March 25, a date the opposition calls Freedom Day. The day marks the brief period of Belarusian independence in 1918, before the country was absorbed into the Soviet Union.