The British fighter was a passenger in a Lexus SUV that collided with a stationary truck on a busy highway linking Lagos and Ibadan in southwest Nigeria on December 29th.
Joshua's backroom team members, Latif Ayodele and Sina Ghami, died in the crash, while the boxer sustained minor injuries.
The incident sparked speculation as to whether Joshua will box again, but promoter Eddie Hearn said Wednesday the 36-year-old would be given all the time he needed to cope with the loss of two key members of his staff.
"I think AJ, as we have seen in the past on boxing-related stuff, is always a brave-face guy, a very positive guy," Hearn told Sky Sports.
"This is very different to that and I know he will take his time.
"He will need his time physically, mentally, emotionally, and spiritually before he makes a decision on his future. I do think he will want to return to boxing, but that will be his decision when the time is right."
The crash happened while Joshua was on holiday in Nigeria following his win against YouTuber-turned-boxer Jake Paul in Miami on December 19th.
Both Ayodele, the personal trainer of the former two-time unified heavyweight champion, and Ghami, Joshua's strength and conditioning coach, died at the scene of the crash.
Before the accident, there was fresh talk of a long-awaited 'Battle of Britain' between Joshua and Tyson Fury, the former world heavyweight champion who recently came out of retirement.
But Hearn said Wednesday: "That is not a conversation that anyone is comfortable having. When the time is right, I believe he will make his decision, and you will hear it from him."
Earlier this month, Joshua paid a moving tribute to "great men" Ayodele and Ghami by saying on Instagram: "Thank you for all the love and care you have shown my brothers."
Nigerian police charged the driver of the vehicle, Adeniyi Mobolaji Kayode, 46, with "dangerous driving causing death".