In 2010, he was the Alphonso Ford EuroLeague Top Scorer Trophy winner and a member of the All-EuroLeague First Team.

Kleiza represented the senior Lithuanian national basketball team in international competitions.

He played on the Lithuanian Junior National Team that won the silver medal at the 2003 FIBA Under-19 World Cup.

The Trail Blazers then dealt his draft rights, along with Ricky Sanchez to the Denver Nuggets in exchange for Jarrett Jack.

The Nuggets' head coach George Karl, said Kleiza played fewer minutes because he is not a playmaker.

Kleiza led the league in scoring, thus winning the Alphonso Ford EuroLeague Top Scorer Trophy, becoming the first Lithuanian to do so.

[12][13] On July 21, 2014, Kleiza signed a one-year deal with the Italian team Olimpia Milano.

[14][15] After the season he withdrew from professionally playing basketball for unlimited period of time due to knee problems, but did not announce his retirement from the sport.

After a poor performance in EuroBasket 2009, Kleiza led his team to a bronze medal in the 2010 FIBA World Championship, averaging 19.0 points, 7.1 rebounds, and 1.4 assists per game.

On July 13, 2017, it was announced that Kleiza received part of the BC Rytas shares from Antanas Guoga.

[19] On February 8, 2020, Kleiza announced his decision to leave BC Rytas due to disagreements with other executives of the team.