Dupont suffered the injury in the 46th minute and was forced off the field at the Stade de Marseille after a clash of heads with Deysel in a clumsy tackle. France thrashed Namibia 96-0 for their biggest ever victory.
Deysel, whose initial yellow card upgraded to a red, was sent abusive messages on Instagram in the comments section of his posts, L'Equipe reported. Deysel's Instagram account has been set to private.
The Namibian Rugby Federation did not immediately respond to a request for comment.
"I would like to extend my best wishes to Antoine Dupont," he told reporters. "Clearly I meant no harm.
"Everything happened very quickly and I couldn’t get my head out of the way quick enough, resulting in a clash. I knew immediately I was at fault.
"I spoke with (France) coach Fabien Galthie (54) immediately after the match and sent my best wishes and apologies to Antoine both personally and via the France team doctor.
"He is a great player and person and I wish him a speedy recovery."
Dupont will remain with the France squad, the French Rugby Federation said on Friday, and will see a specialist to determine how long he will be unavailable.
He looks set to at least miss France's last Pool A game against Italy on October 6th and is in doubt for their potential quarter-final clash against top-ranked Ireland or defending champions South Africa on the weekend of October 14th-15th.
Namibia's final game is against Uruguay on September 27th.
In relation to Deysel's abuse, World Rugby said on Friday that they would "support Namibia in any way possible to stamp out online hate."
On the eve of the tournament the governing body announced a partnership to tackle such incidents focusing on protecting match officials and players by taking action against those who threaten or troll.
At the time, World Rugby CEO Alan Gilpin said: "Rugby is a sport for everyone and we take our responsibility very seriously to make the sport as inclusive, accessible and relevant as possible. This includes sending a strong message that online hate simply will not be tolerated, tackling abuse and harmful content with meaningful action."
