Brondby supporters threw the rodents at Copenhagen defender Ludwig Augustinsson as he went to take a corner.
Leaders Copenhagen won the match 1-0 to open up a 13-point lead over nearest rivals Brondby.
"It's unfortunate that there are some visitors who could not figure out how to behave properly," said Brondby's sports director Troels Bech.
Footage of the incident shows Slovenia international Benjamin Verbic helping team-mate Augustinsson clear at least two rats off the pitch at the 28,000-capacity Brondby Stadium.
Brondby are 10-times champions of Denmark while FC Copenhagen, managed by former Wolverhampton Wanderers boss Stale Solbakken, have won the title 11 times.
A Danish Superliga game between Brondby and FC Copenhagen was marred when home fans threw dead rats at a player.