The 18-year-old, who came through the Saddlers' youth system, made his debut against Tranmere Rovers last December.
Henry has featured 11 times so far this season, scoring his first career goal in the League Cup win over Brighton & Hove Albion, while also finding the net against Scunthorpe United in midweek.
Speaking to the club's official website, Walsall boss Dean Smith was delighted to see the left-back put pen to paper.
"We're really pleased he's signed a new deal," Smith said. "He's a good young player for us and we felt he'd earned the right to a new contract.
"We agreed a deal with Rico and he's signed a new contract for this year and another two. It's really good news for the football club and hopefully he can continue his fine development."
Henry signed his first professional deal at the Banks's Stadium in July 2014.