At least 30 people were caught in the disaster on the BR-376 highway in the town of Guaratuba, in Parana state, according to officials running rescue operations.
Photos from the scene showed red mud and trees cascading across the highway and down a steep cliff, with a number of lorries apparently buried and destroyed.
There have been two confirmed casualties from the mudslides, the fire department said.
There are fears continuing heavy rainfall could cause further landslides elsewhere in the country.
Brazil’s National Institute of Meteorology, INMET, has issued warnings of heavy rain across a number of states.
The BR-277 road has been closed to vehicle traffic toward the coast since Tuesday, cutting off access to the port of Paranagua - a major hub for grains and sugar shipments.
About 80 per cent of goods exported from Paranagua, Brazil’s second-biggest port for grains and sugar, arrive by trucks, the port authority said, declining to estimate losses from the disruption.
Operators and terminals at Paranagua are now moving stockpiled goods that are expected to last until the weekend.