West Ham are 14th in the table and travel to Newcastle United in the Premier League on Saturday, the first of seven games before the earliest expected date of Frederick's return and the opening of the January transfer window.
"Unfortunately we have just one right full back, that is, Pablo Zabaleta," Pellegrini told reporters. "For Pablo, for his age, it's impossible for him to play seven games in December.
"We brought (Fredericks) in to help Pablo, so to be without him is a very serious thing for our defence. First we have to win at Newcastle with Pablo... but we need someone to replace him."
Newcastle are a place above West Ham on goal difference and have momentum on their side, having won their last three games in a row, while Pellegrini's men are coming off a 4-0 defeat by leaders Manchester City.
"Momentum is always important," the Chilean said. "I don't think it's a crucial match for both teams but it's an important match. We need to add points. They are at home and in a good moment but we need to play 24 games more after this one."
West Ham's last 14 league trips to Newcastle have yielded one win for the London side, a 1-0 victory in November 2012, but Pellegrini said he was not concerned by his team's poor record at St. James' Park.
"I don't believe in previous records, if you hadn't told me I wouldn't have known it," he added.
"This is not something that worries me too much, the statistics are there to change and... my mentality is to win every game. We will go to Newcastle to win and not just to draw."
Forward Marko Arnautovic has shaken off a knock he picked up against City and is fit to start, while Andy Carroll and midfielder Jack Wilshere have recovered from ankle complaints.
(Reporting by Simon Jennings in Bengaluru; Editing by Toby Davis)
