Smith received only $1.82 million of his $2.88 million salary and didn't receive $18,500 in bonuses he was due for victories, the Post reported.
The Post, which obtained a copy of Smith's complaint, reported that Chinese basketball team Zhejiang Chouzhou alleges that Smith missed a series of team meetings and skipped practices to travel to Beijing, Shanghai and the United Kingdom.
According to the report, Zhejiang Chouzhou also asked Smith to send his sister, Stephanie, back to the United States because she was "abusive" and "the root" of Smith missing time with the team because the team alleges she made Smith take her shopping.
A FIBA arbitrator in Switzerland will rule on Smith's lawsuit in the coming weeks, the newspaper reported.
Zhejiang Chouzhou, which said Smith "breached" his contract, has until Monday to answer Smith's lawsuit, according to the report.
"It is not possible in the reasonable course of things the player did not attend so many practices [most probably all], held by the club," Smith's attorneys wrote in the complaint, according to the Post. "On the contrary, the player attended many practices and he has presented his excuse for any non-attendances."
Smith's attorneys also said that Smith didn't miss any of Zhejiang Chouzhou's games in the time he was with the team and said in the complaint that the team had the right to terminate his contract if he missed practices, but didn't do so, the newspaper reported.
However, the Chinese team alleges that it didn't terminate Smith's contract only because his agents asked it not to "because it would jeopardize the image of the player for NBA purposes," the Post reported.
Smith, 26, has gained a reputation for being temperamental during his eight-season NBA career and has clashed with teammates and coaches, plus spent time in jail on a reckless driving charge. He also was fined $25,000 earlier this year for posting a photo of a scantily clad woman on his Twitter account.
The Knicks signed Smith in mid-February to a prorated share of their $2.5 million mini-midlevel exception with a player option for 2012-13.
Smith averaged 12.5 points per game on 40 percent shooting, 3.9 rebounds and 1.5 steals in the regular season. But Smith struggled in New York's first-round loss to Miami, shooting 11-for-48 in the final three games of the series.
It is unclear if Smith will pick up his player option or test free agency, a decision he must make by July 1.
Information from The Associated Press was used in this report.