Nigeria international,
The capital club went into the final day knowing a win was required and duly delivered - Alan Dzagoev's 19th-minute strike proving decisive, although goalkeeper Igor Akinfeev was called upon to produce a brilliant double save late on.
Musa scored 13 goals in 29 domestic league games this season as CSKA Moscow finished two points ahead of surprise challengers FC Rostov.
This is Musa's third league title with the club having won in 2013 and 2014.
Rostov won 2-0 at Terek with goals from Christian Noboa and Aleksandr Yerokhin to end two points behind CSKA but will take consolation from a place in next season's Champions League qualifying rounds.
At the other end of the table, Dynamo Moscow were relegated from the top flight for the first time in their history following a 3-0 defeat at home to Zenit.