Bellingham made the breakthrough from the penalty spot in the 30th minute of the contest before turning provider for Kylian Mbappe, with Los Blancos running out 2-0 winners over Jose Bordalas' side.
Real Madrid made a surprising half-time change against Getafe, with Bellingham being replaced by Arda Guler.
Various reports in Spain throughout the second half claimed that Bellingham had been substituted due to dizziness, with the midfielder colliding with Getafe goalkeeper David Soria in the first half of the contest.
Ancelotti said during his post-match press conference that Bellingham had "a problem in his neck", but the midfielder is expected to be fine for next week's La Liga clash with Athletic Bilbao.
Real Madrid's Bellingham suffered neck injury vs. Getafe
"Jude Bellingham? He has a problem in his neck. He will recover in a few days," said Ancelotti.
Real Madrid have now been victorious in their last three league matches, which has left them second in the La Liga table on 33 points, only one point behind leaders Barcelona with a game in hand.
Bellingham has now scored in each of his last three league outings, with the Englishman coming into form after finding it difficult to make his mark in the opening months of the 2024-25 campaign.
Barcelona's recent wobble has pulled Real Madrid back into the La Liga title race, and Los Blancos will be bidding to continue their strong run of form when they travel to Athletic on Wednesday night.
Which players are currently injured for Real Madrid?
Real Madrid could welcome Aurelien Tchouameni back into their squad for their clash with Athletic, with the midfielder in the latter stages of his recovery from an ankle problem.
However, Eduardo Camavinga, Vinicius Junior, Eder Militao, Dani Carvajal and David Alaba remain unavailable for selection.
Camavinga and Vinicius are expected to be back before the end of 2024, but Carvajal and Militao are out for the season with serious knee problems; Alaba is in the latter stages of his recovery from an ACL injury, meanwhile, with the Austrian expected to return in early 2025.