Around 8,000 Irish fans are thought to have been in the Danish capital on Saturday.
“From a police perspective, Ireland are welcome to play at Parken again.
“No episodes were registered with football fans during the night. Thank you,” Copenhagen Police wrote on Twitter.
Set fra et politimæssigt synspunkt er Irland velkommen igen for at spille i Parken. Ingen registrerede episoder med fodboldfans i nattelivet. Tak for det. #politidk— Københavns Politi (@KobenhavnPoliti) November 12, 2017
Extra flights were scheduled between Dublin and Copenhagen to enable fans to travel to Denmark for the match.
The majority had to make to with watching the action on television screens, though, with the Irish football association FAI having only been granted 2,300 tickets.
Enthusiastic fans could be seen and heard in many parts of Copenhagen throughout the day.
The city's many Irish pubs were overflowing by Saturday morning, and Irish flags and patriotic singing were prominent on the Strøget main shopping street.
Both sides remain in with a good chance of making it to the World Cup after the match ended in a 0-0 draw.
The decisive return leg will be played in Dublin on Tuesday.
Saturday's draw means Ireland remain unbeaten against Denmark at full international level since 1985.