Prior to starting college, Musovski was named the NevadaGatorade Player of the Year as a high school junior, and set the state high school record for single-season goals as a senior at 58. At UNLV, he played four years of college soccer, from 2014 to 2017, during which he scored 47 goals in 88 appearances. He was a two-time All-America selection, and as a senior earned WAC Offensive Player of the Year honors.[1][2]
On January 10, 2018, Musovski was selected 30th overall by the San Jose Earthquakes during the 2018 MLS SuperDraft.[4][5] He was signed by the club on March 1, 2018, and immediately loaned to San Jose's USL affiliate, Reno 1868 FC, alongside fellow SuperDraft pick Mohamed Thiaw.[6] Musovski made his professional debut as a second-half substitute for Chris Wehan in Reno's 4–3 loss to Swope Park Rangers on March 17, 2018.[7] He scored his first professional goal in his second appearance on March 24, 2018, in a 1–1 draw with Las Vegas Lights FC, a match from which he was later ejected.[8][9] Musovski was released by San Jose at the end of their 2018 season.[10]
Musovski joined Reno 1868 permanently on January 17, 2019, following his release by San Jose.[11]
On December 10, 2019, Musovski joined Major League Soccer side Los Angeles FC ahead of the 2020 season.[12] He made his debut for the club on July 13, 2020, against Houston in the MLS is Back Tournament as a substitute for Adama Diomande in the 79th minute. On September 2, 2020, Musovski scored his first goal with LAFC in a 5–1 win over San Jose. On October 11, 2020, Musovski scored a brace in a 3–1 win over the Seattle Sounders.
On August 3, 2022, Musovski was traded to Real Salt Lake in exchange for $250,000 in General Allocation Money.[13] His contract option was declined by the club at the end of the 2023 season; according to Musovski, negotiations for a renewed contract had broken down, which led to frustration. He sat out of several matches in the latter half of the season.[14]