Meyler was sent off with Swansea leading 2-1 for catching Naughton with his studs as he chased a loose ball in the 53rd minute.
"We've sent him [Naughton] to hospital for an X-ray," Monk said. "His ankle was really swollen when he came off. We won't know until we get the feedback from that.
"We just hope it's not a serious injury.
"I think it was a genuine 50/50 challenge to be honest. My initial reaction was it was a bad challenge, I don't think there was any malice from the player [Meyler], he didn't go in to hurt Kyle."
Ki Sung-yueng opened the scoring for the hosts in the 18th minute, with a Bafetimbi Gomis brace either side of a Paul McShane goal ensuring all three points for Swansea.
Gomis' first came in magnificent fashion courtesy of an excellent close-range scissor-kick, with his second a delicate lob over Allan McGregor in injury time as Hull flung bodies forward in search of a leveller.
"This is the reason why I brought him [Gomis] to the club," Monk added. "I know the quality he has and you saw an excellent striker scoring some very good goals, very good finishes.
"He's confident. Strikers are always confident when they score goals. He's got all types of finishes.
"He's played in the Champions League [for Lyon]; he's very strong; he's very good technically in the air. Very pleased for him."
