Wilson suffered the injury in the first half of the Magpies’ 3-2 victory over Southampton in the Premier League last weekend.
The 28-year-old joined Newcastle from Bournemouth for £20m at the start of the season and he has scored 10 top flight goals in 21 appearances while providing five assists.
Newcastle travel to Stamford Bridge to take on Chelsea in the Premier League on Monday, and manager Steve Bruce announced the bad news in pre-match news conference.
"Callum Wilson has got a tear to his hamstring so that could be six to eight weeks [out]," the Newcastle boss said, while also confirming that Fabian Schar and Javier Manquillo will be out for a similar amount of time.
"Fabian Schar [also] has had an operation on his knee ligaments so it's eight weeks out for him. Javier Manquillo did his ankle ligaments so he could be a similar time out.
"The aftermath of Saturday's game, losing three players including your centre-forward for weeks is a bitter pill to swallow.
"We hoped it was a grade one but unfortunately it's worse than that. We don't think he needs an operation but it takes time."
Newcastle are 16th on the Premier League table, 10 points above the relegation zone.
