The group from the movement known as "You Stink" posted a video of about 30 demonstrators sitting cross-legged on the floor, clapping and shouting slogans against the minister, Mohammed Machnouk.
"Out, out, out!" they shouted Tuesday . It was not immediately clear whether the minister was inside the building, the Associated Press news agency reported.
Following a huge protest in downtown Beirut on Saturday, the group issued several demands including the minister's resignation, threatening to escalate action if he does not.
The minister has refused, resigning only from a government committee assigned to resolve the trash crisis.
Angry protests over the government's failure to deal with the garbage crisis have evolved into the most serious anti-government protests in Lebanon in years. The protesters seek to challenge an entire political class that has dominated Lebanon since its civil war ended in 1990.
The protests have attracted supporters from across Lebanon's political and religious divides in a reflection of the growing frustration with an aging and corrupt political class that has failed to provide basic services.
So far the only response to the growing protest movement has been a promise by the parliament speaker for high-level talks between Lebanon's politicians in the coming days.