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.

Police reportedly fired teargas at mourners. Kashmir is under lockdown as protests against Indian rule continue.
More than 80 people, nearly all anti-government protesters, have died in more than two months of violence.
Nasir Shafi was found dead after going missing on Friday in Srinagar.
An almost complete curfew is now in place in Kashmir, part of the Muslim-majority Jammu and Kashmir state.
Why has Kashmir erupted in violence?
Some reports say Nasir Shafi was 11 years old.
Correspondents say restrictions on free movement and internet use are at their tightest since street demonstrations began on 9 July.
They were sparked by the killing of a popular militant leader in a gunfight with the army.
Security forces have continued to fire lethal shotgun pellets at protesters, despite the government saying it would use an alternative.
Disputed Kashmir is claimed in its entirety by both India and Pakistan and has been a flashpoint for more than 60 years, causing two wars between the neighbours.
A Danish Superliga game between Brondby and FC Copenhagen was marred when home fans threw dead rats at a player.
[NEXT_CONCEPT]
Thousands of people have defied a curfew in Indian-administered Kashmir to attend the funeral of a schoolboy whose body was found riddled with pellet wounds, local media report.