Sakho, who joined Palace on a six-month loan from Liverpool in January, twisted his knee while tackling Harry Kane early on in the second half at Selhurst Park.
The France international received lengthy treatment on the pitch before being stretchered off while wearing a knee brace.
The 27-year-old will undergo a scan to assess the extent of the injury on 27 April.
"We think it's a ligament, but which one we don't know," Allardyce told Palace's official website.
"We certainly hope it's not the cruciate but it could be the medial or the lateral, but it certainly looks like a hyper-extension of the knee and we wait and see what the scan shows.
"With such a short space of time left we won't know if any of our defenders will get fit again and we might have to rely on Damien [Delaney] and Martin [Kelly] for the remaining games of the season."
Sakho fell out of favour under Reds boss Jurgen Klopp at Anfield, but has impressed in his brief loan spell at Palace.
Earlier this month, the 27-year-old said he had not given up hope of having a future at Liverpool.
"I still have three years on my Liverpool contract. If I have to wear the Liverpool shirt again, I'll do so with pleasure. If I have to wear another shirt ... we'll see," he told Telefoot.
However, the Frenchman angered Liverpool fans by celebrating Palace's 2-1 win over Liverpool at Anfield on 23 April.
He later insisted that his celebratory handshake with Christian Benteke during the game was not meant to cause offence to Liverpool supporters.
"There was nothing behind it, nothing else to imply by it," Sakho was quoted as saying by the Guardian.
"Just two friends who are playing for the same team and who have the same goal, which is to get the three points at each game to make sure the team stays in the Premier League."