The three-time Women's Champions League victor with French side Lyon was named the world's best female player of 2018 at a gala in Paris on Monday.
The 23-year-old Lyon and Norway striker became the first victor of the prize, which recognises the world's best player, at an awards ceremony in Paris.
Hegerberg, one of seven players from the all-conquering Lyon side to feature among the 15 nominees, dismissed suggestions that the night was marred by the "twerk" request.
Solveig used social media to send Hegerberg an apology and give his take on the incident.
Real Madrid and Croatia midfielder Luka Modric claimed the 2018 Men's Ballon d'Or Award, breaking Cristiano Ronaldo's and Lionel Messi's 10-year winning streak.
"This award is for all the players who probably deserved to win it and didn't".
Solveig has been widely condemned, and Murray's was among the strongest of the condemnations.
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". I've been invovled in sport my whole life and the level of sexism is unreal.
Speaking after collecting her award on Monday, she told the Associated Press that she has no plans to reverse that decision.
Speaking to BBC Sport, she said: "He came to me afterwards and was really sad that it went that way".
Prior to Monday, Ronaldo and Messi had each won the Ballon d'Or five times dating back to 2008.
Murray has been a staunch supporter of equality in tennis, too.
Accompanied by a video apologising further to Hegerberg, Solveig wrote on Twitter: "Sincere apologies to the one I may have offended". I want to end this speech with a message to all young girls in the world.
But Hegerberg says she does not consider the incident to be "sexual harassment".
Solveig played music and danced throughout the ceremony.
Also on Monday, Mbappe was named the first-ever victor of the Kopa Trophy as the world's best under-21 player.
This year marked a new era for the Ballon d'Or, as France Football handed out the inaugural women's honour. The victor was chosen by a group of 40 voters - a different group than the judges for the men's award. Hegerberg, who previously became the first woman to win the Norwegian Gold Ball for the best footballer in Norway, thanked her teammates, her coach and the president of the club, Jean-Michel Aulas. "Only experts can vote", he said.
It remains to be seen if she will return to the national set-up in time for next year's World Cup, which will be played in France with the final in Lyon.