Vrána made his Elitserien debut playing with Linköping HC during the 2012–13 season. After the 2014 draft, Vrána signed his first NHL contract with the Capitals, a three-year entry level deal on 15 July 2014. On 29 November 2016, he received his first NHL callup from the Hershey Bears. He made his NHL debut on 1 December against the New York Islanders. Vrána scored his first NHL goal on 9 December 2016 against the Buffalo Sabres. He was reassigned to the Bears on 1 January 2017.