Lavezzi, who joined Hebei CFFC from Paris St Germain in a multi-million dollar deal last year, was pictured making the gesture while in team uniform, and both the player and the club released statements in an attempt to diffuse the situation.
"Per the request of the Chinese Super League, we took the official photos for the season," Lavezzi said in a statement issued on Sunday.
"We were given instructions by the official photographer and I was trying to make some interesting photos by making some funny faces, which would be used afterwards for entertainment purposes.
"I had no intention of insulting the Chinese people and did not do it with any bad intentions," the 32-year-old added.
"I'm very happy to be here as part of the Hebei club. I have had great time here with my team mates and it has been a great journey. Every Chinese person around me is friendly and I love my life here.
"I deeply apologise if this photo has offended the Chinese public and fans. I will be more careful in the future."
Lavezzi joined Hebei in February last year in a deal reported to be worth around 10 million euros (8.47 million pounds) per season, but his involvement in his first year with the club was curtailed due to injury.
He has been in impressive form in recent weeks, however, and scored in a 1-1 draw with Guangzhou R&F on Friday as Hebei, coached by former Manchester City manager Manuel Pellegrini, moved up to fourth in the Chinese Super League standings.
"Since joining us at the beginning of 2016, Lavezzi has been getting along very well with the team and been loved by fans too," said Hebei, who also denied the pictures had been officially released by the club.
"He has expressed his love for China many times too. Now we have communicated with him and have clarified he had no bad intentions and he deeply apologised for any offence caused.
"As a club we apologise for our neglect in our work. We will be more careful in the future."
(Reporting by Michael Church in Hong Kong; Editing by John O'Brien)
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