Biggar, who kicked four penalties when Wales beat Italy last week, lasted only 19 minutes at Franklin's Gardens before limping off in Northampton's 67-17 victory.
Biggar's left knee was heavily strapped but Boyd told reporters after the game the decision to replace him had been a precautionary one.
"He probably could have played on," Boyd told reporters. "He came back from Italy with a really, really low-grade MCL (medial-collateral ligament) strain in the knee and was keen to play.
"He didn't train on Tuesday and he trained on Thursday and trained really well and felt really comfortable.
"He just tweaked it again, he probably could have stayed on but that at that stage we thought we'd bring him out.
"I'm not a medical man but I don't think there's any reason that he won't be (in contention for next week)."
Biggar is vying with Cardiff's Gareth Anscombe for the Wales number 10 jersey ahead of England's visit next Saturday.
England lead the Six Nations on 10 points after two bonus-point victories, with Warren Gatland's Wales also unbeaten but on eight competition points.
(Reporting by Martyn Herman and Greg Stutchbury; Editing by Toby Davis/Peter Rutherford)
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