The midfielder has been widely linked with a move to West Ham this summer, and speculation over his future increased when he missed the 1-1 draw with the Seagulls.
But Hughton has insisted the Scotland international was not in attendance due to a "family issue", and he expects Snodgrass to rejoin the squad by the end of the week.
"It's very simple and I can set the record straight," said Hughton. "It's a family issue.
"He will be with us hopefully on Wednesday and certainly on Friday. It's very much a personal issue."
Newspaper reports in Scotland have suggested that Snodgrass returned to Scotland on Tuesday following a car crash involving his pregnant partner.
Hughton said earlier this week that he was confident of holding onto Snodgrass, who was one of the Premier League's most consistent performers last season following his move to Carrow Road from Leeds.
"We want to ensure we keep hold of our best players and we are a club at the moment that doesn't need to sell," Hughton said.
"We are looking to strengthen and not let players go. He (Snodgrass) is definitely a player who is very much in our plans."