The 32-year-old, who represented his country as an over-age player at last year's Beijing Olympics, was also fined 40,000 yuan ($5,900) for spitting at the official after being shown a yellow card in last weekend's match against Qingdao.
"This was a serious violation and he had been punished many times by the club for his irrational behaviour on the pitch," said a statement on the club website.
"His behaviour constituted a serious breach of contract and the club have therefore cancelled his contract."
Zivkovic joined Shandong in 2006 and played a key role as an attacking midfielder in Luneng's double-winning campaign of that year as well as last season's title triumph.
"On behalf of the club, I would like to express our appreciation of his contribution but our players must take this as a warning," said Han Gongzheng, the club's deputy manager.
Zivkovic was one of seven players and club officials handed stiff penalties by the Chinese Football Association (CFA) for various offences in matches last weekend, FIFA's designated Fairplay Day.
"My biggest regret is that I can't go for the title with my team mates ... I hope I can find a Chinese club to play for until I retire," Zivkovic told the Beijing News.
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