The purchase is the first in the West by a Chinese company of a work by the Spanish artist.
"We are happy to have bought the work at this price, especially with the slowdown in the global economy, because another of Picasso's paintings, 'Boy with a Pipe,' sold for $104.16 million in 2004," Guo Qingxiang, who manages Dalian Wanda Group's art collection, said.
The painting, which had an estimated starting bidding price of $12 million at the auction, was "one of Picasso's favorites" and was on display "in his studio until his death", Guo said.
"Claude et Paloma", which was completed in 1950, shows Picasso's daughter at nearly the age of one with her three-year-old brother.
The painting was part of a private collection that went on the auction block on Monday in New York and performed below expectations.
Wang Jianlin, who Hurun magazine ranked as China's richest person in August with a net worth of more than $22 billion, continues to expand his art collection, which includes works by leading Chinese artists Wu Guanzhong, Shi Qi and Li Keran, Guo said.