
The centre-back was stretchered off late in the heartbreaking 2-1 defeat at Hill Dickinson Stadium after crumpling to the ground following an innocuous tussle with Cody Gakpo.
It was a devastating blow that took the wind out of Everton, who went to lose in the final minutes of the 11 added on - some of which were due to the treatment required by Branthwaite.
Asked whether he had any news on the England international in the post-match press conference, Moyes said: “No, but I am worried though.”
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In a separate interview the Blues boss added: "Jarrad was probably the best player on the pitch at times today. I thought he played so well.
"I’m worried it could be serious, but we’ll need to wait and see."
Branthwaite’s season has already been decimated by injury.
The 23-year-old missed the opening five months of the campaign with a hamstring problem that eventually required surgery.
After picking himself up from turf following the collision with Liverpool forward Cody Gakpo he looked to the sky in anguish before collapsing.
It was one of two potentially serious injuries in the game with Reds goalkeeper Giorgi Mamardashvili also stretchered off.
Liverpool head coach Arne Slot later said Mamardashvili had been taken to hospital after he was caught by Beto and Andy Robertson amid Everton’s second-half equaliser.