Vrána is a native of Sternberk and logged his first minutes in the Czech Extraliga with HC Havirov during the 2001-02 season and moved to Canada for the following year, joining the Halifax Mooseheads in the Quebec Major Junior Hockey League.

He remained with the Mooseheads until the end of the 2004-05 campaign and then gained three years of AHL experience with the Albany River Rats and the Lowell Devils.

[2] Vrána returned to the Czech Republic in 2009, signing with HC Vítkovice where he would play until 2011, when he agreed to terms with Amur Khabarovsk of the Kontinental Hockey League (KHL).

On July 2, 2014, Vrána left HC Lev, after it declared bankruptcy and folded, as a free agent to sign with fellow KHL club, Atlant Moscow Oblast.

Vrána signed with Brynäs IF of the Swedish Hockey League (SHL) for the 2015-16 campaign and left Sweden after the season to join HC Sparta Praha of the Czech Extraliga for 2016–17.