The incident was a major talking point despite Hegerberg's achievement in becoming the first victor of the women's Ballon D'Or, an award which has been handed to male footballers since 1956.
The Norwegian seemed briefly non-plussed before joining in a more conventional waltz on stage as the audience looked on in embarrssment.
Hegerberg won the Women's Ballon d'Or after scoring a record 15 goals in the UEFA Women's Champions League, which she won with French club Olympique Lyonnais.
"I didn't feel it was like that at all to be honest and I am sad if people thought about the situation like that", Hegerberg said after the show.
"It was the most important people in my life - most of them, some of them were missing - but I am so happy to share this moment with them".
Hegerberg said Solveig also apologised to her personally, even though "I wasn't upset".
He also added that he duly explained to Hegerberg that his twerking proposition was a "joke". They have existed since 1956 but had not previously had a women's football category.
Luka Modric saw off competition from France's World Cup stars as the Real Madrid and Croatia midfielder won the Ballon d'Or on Monday to end a 10-year stranglehold on the award by Cristiano Ronaldo and Lionel Messi.
What was a huge step was taken back a notch and unfortunately Hegerberg, as with everyone watching, is reminded that no matter how high up a woman goes or what new ceiling is broken there will always farther to go.
The 25-year-old Australian worldwide striker was nominated after starring for clubs - Perth Glory and Chicago Red Stars - and country, winning the Golden Boot as top scorer in Australia's W-League and American NWSL.
The award crowned a fantastic 2018 for the 23-year-old, who scored in this year's Champions League final as Lyon routed Wolfsburg 4-1. Sometimes you have to take tough decisions to stay true to yourself. "We just follow two different paths at the moment", she said.
France Football magazine has been awarding the Ballon d'Or - until now only to men - since 1956, when Matthews was the first victor.