The fighting between Bosian Croats and Muslims broke out around midnight after Croatia lost the match 1-0 to Brazil.
The Bosnian Croats had been celebrating what was regarded as a good performance by the Croatian team against the Cup favourites.
Police officials say a group of Bosnian Muslims, who had been backing Brazil, then started taunting the Croats, sparking clashes betwen the two groups.
Rocks were thrown, several houses and vehicles were damaged and one Muslim man was seriously wounded after being shot by an unknown gunman, Srecko Bosnjak, a Mostar police spokesman, said.
Some 26 people were arrested during the clashes, he added.
"We plan our activities in accordance with the World Cup schedule," said Bosnjak. "Every Croatian match is a high risk event here."
Damage from the night's fighting was "enormous", he said.
The 1992-95 Bosnian war left the Catholic Croats, Orthodox Serbs and Muslim Bosniaks divided into a Bosnian Serb ministate and a Muslim Croat federation, Bosnia-Herzegovina.
The town of Mostar itself is divided into a Bosnian Croat section on one side of the river Neretva, and a Muslim section on the other.
The town was the scene of fierce fighting during the war, leaving thousands dead and destroying a famous medieval bridge across the river.
The bridge has since been rebuilt, but rebuilding ties between the town's communities has proved harder.
With the World Cup under way, much of the Croat section is decked out in the red and white check of the Croatian team.
In the Muslim side however, locals usually back any other team that is playing Croatia.