Fights erupted and people vomited on the platform around 1 a.m. Wednesday in Copenhagen, causing trains to be delayed, the Swedish news agency TT reported.
Hundreds of travelers were stuck on the platform, TT reported, and about an equal number took cabs to Malmo, Sweden.
Danish rail operator DSB has been criticized for not adding extra trains despite huge Swedish interest in the Madonna's "Sticky & Sweet" tour.
DSB said they added five cars to their trains to respond to the extra demand Madonna's concert Tuesday brought.
"We used all the capacity we had available," DSB spokeswoman Irene Lippold said. "We have to keep the other trains running as well."