Mamukashvili first played for Armia during the Georgia Championship; he went on to feature in Georgia's 2012 European Nations Cup squad, making his debut against Spain.[1] Mamukashvili also appeared in the sides 2012 end of year tour campaign.
On 15 August 2014, Shalva signed a contract to join Sale Sharks in the Aviva Premiership in England from the 2014–15 season.[2] On 11 November 2015, Shalva signed a contract to join Glasgow Warriors until the end of the 2015–16 season.[3]
In 2020, he returned to England to join Leicester Tigers ahead of the 2020-21 season.[4] On 23 February 2021 Leicester announced that they had come to an agreement with Shalva to release him from his contract early.[5]