The striker went under the knife earlier this week to repair a damaged hamstring.
The former Crystal Palace and Sheffield Wednesday man was injured few minutes into his full debut against Cheltenham in the Carabao Cup.
Wickham had made one substitute appearance in the Championship for North End before the injury.
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He was caught from behind by a challenge when his leg was fully stretched, causing damage to the higher part of the hamstring in his right leg.
After seeing a specialist, Whickham has undergone surgery on the injury and posted a message on Instagram.
He said: “To say I’m gutted is an understatement but I’m grateful to have been in the hands of the best, the surgery was a success and I’m already on the road back.
"I know I’ll give everything I get back on the pitch as soon as possible. Thank you to everyone who’s reached out in the past few days. Much love CW21.”
Wickham signed a four-month contract at North End earlier this month, having trained with them as a trialist in a bid to earn a deal.
He enjoyed a four campaign stint at the Stadium of Light – with loans at Leeds United and Sheffield Wednesday in between – following an £8m move from Ipswich Town back in 2011.
The fee broke Ipswich's record for transfer fees recouped, and broke the transfer record for an EFL player moving to a Premier League club at the time.