Kate ensured she waved to fans who had turned out to welcome the royals before the couple headed inside.
The musical, which won six Tony Awards after opening on Broadway in 2016, is about an anxiety-ridden boy struggling to connect in a hyperconnected world.
Once inside the foyer, the royal couple chatted about the mental health theme to the play’s author, Steven Levenson, and composers Justin Paul and Benj Pasek.
“Ten years ago, do you think this play would have been here?” William asked.
“I don’t think it would have even existed,” Mr Pasek said.
The couple’s outing comes after rumours began swirling that William and Kate are set to avoid a major event being held by Prince Harry and Meghan Markle this year.
A royal insider told The Sun the Duke and Duchess of Cambridge are likely to keep their distance from the Sussexes, who will be hosting the Invictus Games in the Netherlands in May.
While Harry and Meghan will no doubt be present at many of the events, the source claimed that it’s unlikely William and Kate will venture across the channel.
“William had not been expected to attend even before the news broke about Harry and Meghan’s decision to step away from public life,” the source said.
Despite a lack of other royal members at the sporting event, the insider claimed it doesn’t necessarily mean there is bad blood between the brothers.
“It is highly unlikely that he [William] and Kate will be a part of the event in any way. But it isn’t a snub. The entire Royal Family remain hugely supportive and very proud of Harry’s work on Invictus and think it is a wonderful event,” the source said.
“It’s very much in Harry’s vision although he has regularly turned to his father for advice and support over the years. It is unlikely to be any different this time round but Harry will be front and centre.”
Wills has also been a strong supporter of the Invictus Games, and was present, along with his father Prince Charles, at the opening ceremony at the first games in London in 2014.