The setback comes after the youngster was forced off during last week's 1-0 defeat to Manchester United, compounding a difficult spell for a side already in turmoil following a major managerial change at Stamford Bridge.
McFarlane delivered the update ahead of Sunday's FA Cup semi-final against Leeds United at Wembley, describing the injury as a significant disappointment for both the player and the club.
"Estevao, unfortunately, won't play for us this season," he said. "He's going to be out for a little bit of time. That's really unfortunate, especially for someone so young and so talented, but we're here to support him and be around him."
Asked whether the winger could recover in time for the World Cup in Canada, Mexico and the United States, McFarlane was cautious.
"I'm not sure on that, if I'm honest. I just know he won't be available for us, so I'm sure he's very hopeful he can make the World Cup, but I don't know on that."
Pep Guardiola has confirmed Rodri will not feature in FA Cup semi-final action against Southampton at Wembley on Saturday, with Manchester City opting for caution as the midfielder continues his recovery from a groin injury.
Bukayo Saka and Riccardo Calafiori are set to hand Arsenal a timely boost ahead of a pivotal Premier League clash with Newcastle United, as the title race enters its decisive phase.
Chelsea have sacked head coach Liam Rosenior after just 106 days in charge after the club slumped to it's fifth consecutive Premier League defeat against Brighton on Tuesday.
Roberto De Zerbi says he has developed a "special connection" with Xavi Simons as he looks to get the best out of the Tottenham playmaker during the club's relegation battle.
