On 23 November 2012 Cibicki signed a first team contract on a youth basis with Malmö FF. Cibicki made his Allsvenskan debut for Malmö FF in a home fixture against Gefle IF on 7 July 2013. In total Cibicki played seven matches for the club during his first season, most of the matches coming on as a substitute for the attackers. On 1 July 2014 Cibicki signed a first team contract with Malmö FF for three and a half additional years at the club. Previously in the summer of 2014 Cibicki had reached a verbal agreement with Dutch Eredivisie club FC Groningen, but he decided to stay at Malmö FF the day before the deal was about to be signed.
Cibicki holds dual passport, from his country of birth Sweden and his parent's birth country Poland. In March 2013 he was called up by the Poland national under-19 team for two friendlies against Georgia. Cibicki played for 24 minutes after coming on as a substitute in the 3–1 win against Georgia in the first of two friendlies.