Feliks Khojoyan has debuted in his hometown club Shirak as a professional player in 1994. In that season he played 13 matches and won Armenian Top League gold medals. Since that period, he has consistently played in the team, which has won all domestic titles in Armenia.At the end of the 2000 season, Khojoyan left Shirak and moved to Araks from city Ararat and after to Banants where he managed to play only 2 matches and moved to the Iranian First League club called "Pegah Gilan". The contract was signed with the club for six months. Iranian club was soon promoted to the Top League and extended Khojoyan's contract by 2 years. At the end of the 2004-05 season, Pegah Gilan was again relegated from the Top League, and Khojoyan moved to another First League club Esteghlal from Kish. Financial difficulties of new club forced Khojoyan to return to Armenia. After a long break, Khojoyan returned to his native "Shirak", where he intended to finish his professional career which happened in December 2009.
In season 2010 Khojoyan joined the coaching staff of Shirak as an assistant coach to Vardan Bichakhchyan. As a coach, Khojoyan became the champion of Armenia (2012/13), twice won the Armenian Cup (2011/12, 2016/17) and the Armenian Super Cup (2013/14/, 2016/17). Feliks Khojoyan has a UEFA Coaching PRO License. In July 2020 Feliks move to Ararat as Vardan Bichakhchyan's assistant.