Tan, who slammed into Yang's knee at full speed late in the Chinese Super League (CSL) fixture, was also fined 25,000 yuan, the Chinese Football Association announced on its official website.
"I feel really frustrated," Tan told the West China Daily newspaper. "I did not think (the challenge) was that bad."
The CFA also warned the manager of Beijing's Workers' Stadium, where spectators at Saturday's match were injured by flying missiles and visiting players harassed by home fans with laser pointers.
The 64,000-seat stadium will host England's Tottenham, West Ham and Hull in the Premier League Asia Trophy next month.
A Guoan Club official said he was sorry that Tan's punishment was not more severe as the CFA had pledged a zero-tolerance policy on violent tackles before the season started.
"I can only say I am unhappy and it is unfair," said Beijing Guoan president Luo Ning, adding that the club did not plan further action as Yang was not seriously hurt.
The 23-year-old Tan has a record of violent challenges, prompting Chinese internet forums to dub him "Kicking Tan".
He was sent off at last year's Olympics for kicking a Belgian player in the groin. Three months later, Tan's tackle on a Beijing player started a mass brawl which prompted state television to stop broadcasting CSL games.
Beijing lead the CSL after 11 rounds while Tianjin stand eighth.
