The fire department said that units were on the scene of the construction site, but had no further details.
Webcam footage from the building site showed black smoke rising from the structure, known now as the Humbolt Forum.
The Forum told the dpa news agency that it appears that a vat of roofing tar exploded outside the building and started the blaze.
The palace, originally built in the 15th century and finalized in the 18th century, was largely destroyed during World War II and then demolished in communist East Germany.
A modern version with replica facades is now being built on the site with scheduled completion later this year.
The interior will house a 40,000 square-meter (430,000 square-foot) cultural and exhibition center.