The Duchess is said to be distantly related to a Red Sox player
The couple attended the first of two matches which are held in the UK as part of a push to promote the American sport.
It was a rare appearance for US-born Meghan, who has been on maternity leave since the birth of her son Archie on 6 May.
Before the match, they were presented with a personalised baby Yankees shirt and Red Sox bodysuit for the infant.
During her visit, Meghan greeted Red Sox outfielder Mookie Betts, who is reportedly a distant relative of the Duchess.
He told Fox News that he was hoping to meet her, and when he did he gave her a hug and she even invited him to dinner.
Meanwhile the Duke of Sussex admitted to not knowing all that much about the sport, reportedly asking Red Sox players: "I’m not that current with baseball – who normally wins?"
Although MLB matches have taken place outside of the US in the past, this is the first regular-season MLB game to be played in Europe.
MLB vice-president of international strategy Charlie Hill said: "We want more people aware, playing and watching our sport."
The game is part of a three-day American-themed festival which will take place in east London.