Tsvetanov was part of the Bulgarian under-19 team that played at the 2008 Union of European Football Associations European Under-19 Football Championship in the Czechoslovakian Republic. Spartak Pleven
Born in Pleven, Tsvetanov began his career playing for his local club Spartak. On 9 September 2006, at the age of 16 he made his professional debut in the West B PFG, playing the second half of a 3–0 defeat to Minyor Pernik.
He scored his first goal on 7 April 2007 against Hebar Pazardzhik in a 2–0 home league victory.
He made 15 league appearances, scoring three goals during his debut season. The following season Tsvetanov scored four goals in 12 matches.
In January 2008, Tsvetanov joined Litex Lovech on a four-and-a-half year contract for an undisclosed fee. He made his competitive debut in the A PFG in a 0–0 draw against CSKA Sofia on 1 March 2008.
He played for 45 minutes.
After six years in Lovech, Tsvetanov surprisingly signed a two-year contract with Botev Plovdiv as a free agent on 21 August 2014. Momchil Tsvetanov played in 14 games in A Grupa and 3 games for the Bulgarian Cup without scoring any goals and without making any assists. He failed to impress and at the end of the season his contract was terminated by mutual agreement.
On 30 June 2015 Tsvetanov joined CSKA Sofia.