[2] Blaswich started his career at Borussia Mönchengladbach, where he was loaned out to Dynamo Dresden,[3] and Hansa Rostock.

[5] On 15 February 2022, Blaswich signed a contract with RB Leipzig, effective from 1 July 2022 to 30 June 2025.

[7] On 5 October 2022, during a Champions League matchup against Celtic, Leipzig's longtime keeper Péter Gulácsi suffered a torn ACL rupture, which would force him to miss the rest of the season, in which Blaswich immediately replaced him in the 13 minutes of the first half, in a match which ended in a 3–1 victory.

[10] On 22 June 2024, Blaswich joined Austrian Bundesliga side Red Bull Salzburg on a season-long loan deal.

[11] In November 2023, Blaswich was called up for the Germany national team by coach Julian Nagelsmann, ahead of their friendly matches against Turkey and Austria.