Solveig sparked outrage when he seemingly asked Lyon striker and Norway global Hegerberg to twerk on-stage after the 23-year-old became the first ever female victor of the award on Monday.
Then, as she was leaving the stage, French DJ and co-host Martin Solveig asked her if she could twerk, but the three-time women's Champions League victor abruptly said "no" before walking away.
Responding to the criticism, Solveig tweeted: "Sincere apologies to the one I may have offended".
"I'm a little amazed and astonished by what I'm reading on the internet", he said in a video. This comes from a distortion of my English level, and my English culture level which obviously isn't enough because I didn't mean to offend anyone. "And I want to apologize to the ones I may have offended".
Hegerberg told the AP after the ceremony she was not upset by the request, confirming Solveig apologised afterwards, saying: "I didn't take it like that at all to be honest".
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After winning the award, Hegerberg expressed her pride at having won the Ballon d'Or's first female award and shared some words of encouragement for other young women around the world.
She answered with a simple "no" to the question, which was asked by French DJ Martin Solveig, before turning to walk away.
The decorated Hegerberg, whose trophy cabinet already boasts a UEFA Best Women's Player award and BBC Women's Footballer of the Year honor, beat out fellow stars Dzsenifer Marozsan, Marta, Sam Kerr, and Pernille Harder to capture Monday's inaugural crown.
After the event, Hegerberg told reporters that she had accepted an apology from the 42-year-old. "I didn't really consider it sexual harassment or anything in the moment".
He was widely criticised for his question to Hegerberg.
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Croatia and Real Madrid midfielder Luka Modric was named the best men's player of 2018 at the prestigious awards organised by France Football magazine.
He concluded his message by referring to a "level of sexism unreal".
The two-time Wimbledon victor and Olympic double gold medalist added: "And to everyone who thinks people are overreacting and it was just a joke".
A soccer star who was honored as the world's best female player on Monday was asked to twerk on stage just moments later. "It was more of a joke of making her dance", she added. "The Ballon d'Or is the most important thing". "It's all about how we respect women's football".
"I think that a lot of education still needs to be done".
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She helped her team, Lyon, snare a Champions League title for a record fifth time, scoring 15 goals, according to AFP.