Mr Weah told hundreds of supporters at a rally on Sunday that he would block January's inauguration of Mrs Johnson-Sirleaf as president.
"There is no victor for now, and I say there will be no inauguration in the country until the world gets together and finds a means for a peaceful resolution to the problem," he said.
Supporters chanted "No George Weah, no Liberia".
Riot police were deployed on the streets and made several arrests. The United Nations Mission in Liberia also deployed UN police.
Mrs Johnson-Sirleaf is set to become Liberia's first elected head of state since the end of 14 years of war in 2003.
She will be Africa's first elected woman president.