After helping lead CSKA Moscow to the EuroLeague final in 2012, Shved spent three years in the NBA, before returning to Europe and earning an All-EuroLeague Second Team selection in 2018.

Shved began his professional career with CSKA Moscow in a Russian Super League game, against Ural Great Perm, on November 4, 2006.

[citation needed] On July 23, 2012, CSKA Moscow announced the departure of Shved in order to sign with the Minnesota Timberwolves of the NBA.

As part of the deal, Shved and teammate Luc Mbah a Moute were traded to the Sixers, along with a 2015 first round draft pick from Cleveland.

[6] On December 19, 2014, Shved was acquired by the Houston Rockets in a three-team trade that also involved the 76ers and the Minnesota Timberwolves.

[14] In 2017–18 season, Khimki made it to the 2018 EuroLeague Playoffs quarterfinals, where they were eliminated by CSKA Moscow, with 3–1 series result.

[16] On August 12, 2021, Shved officially returned to CSKA Moscow of the VTB United League, and of the EuroLeague until it was suspended due to the 2022 Russian invasion of Ukraine, signing a two-year (1+1) deal.

At the 2012 Summer Olympics, on August 12, 2012, Shved scored 25 points, to lead the Russian national team to an 81–77 victory, over Argentina, in the bronze medal game.