Michal Škvarka

In July 2011, Škvarka joined Slovak club Zemplín Michalovce on a one-year loan from Žilina. He made his league debut for Michalovce against Ružomberok B on 31 July 2011. On 19 June 2019, Škvarka joined Ferencváros on a three-year contract for a sum of 200 thousand Euros. It was also revealed that Ferencváros had seriously contented for his services even in winter of 2018–19 season, but the transfer did not take place due to Škvarka's injury. On 16 June 2020, he became champion with Ferencváros by beating Budapest Honvéd FC at the Hidegkuti Nándor Stadion on the 30th match day of the 2019–20 Nemzeti Bajnokság I season.

Wisła Kraków

On 6 July 2021, Škvarka's arrival to Polish Wisła Kraków was announced on a two-year deal, with an option for a one-year extension, as a free agent, where he was to be coached by Adrián Guľa - his ex-manager from Žilina. He left the club by mutual consent following its relegation to I liga.

In 2017, Škvarka was called up to the senior national team for two unofficial friendly fixtures held in Abu Dhabi, United Arab Emirates, against Uganda and Sweden. He debuted against the former opponent, playing from the start and playing the entire match as Slovakia went on to lose the game 1–3. Škvarka also played the first half of the match against Sweden (0–6 loss), when he was replaced by Martin Bukata.

Žilina

Fortuna Liga: 2009–10, 2016–17 Slovak Cup: 2025–26 Ferencváros

Nemzeti Bajnokság I: 2019–20, 2020–21 Individual

Fortuna Liga Player of the Year 2016-17