The Ineos rider, who won the Giro in 2020, was riding with his team-mates including overall leader Geraint Thomas who also hit the deck but managed to continue.
British rider Geoghegan Hart, third in the overall standings, was attended to by medics before being loaded into an ambulance.
Race favourite Primoz Roglic was also involved in the crash but managed to continue on a Jumbo Visma team-mate's bike.
Shortly afterwards, Movistar rider Oscar Rodriguez suffered a crash in which he came into contact with a roadside sign.
This year's weather-affected Giro has been hit with several high-profile withdrawals with former race leader Remco Evenepoel having to abandon after testing positive for COVID-19.
Wednesday's stage is the longest in the race, a 219km ride from Camaiore to Tortona.