The Fiorentina star was about to take a corner when he was barraged by missiles from the end where a number of West Ham fans were sat.
They included beer cups and vape pens with one making contact in a shocking way.
One hit him on the back of the head and caused a nasty cut, which caused him to bleed profusely.
The match had to be halted as a result while the left-back was strapped up with a headband.
Speaking on talkSPORT, Sam Matterface condemned the action, saying live on air: "This is absolutely mindless. Paqueta, Coufal and Aguerd have gone over to the West Ham fans and said, 'calm down'.
READ MORE ON WEST HAM
West Ham fan zone turns into Glastonbury and Hawkes sings iconic chant in Prague takeover
West Ham fans sing 'class' Lucas Paqueta chant on way to Europa Conference League final
"Michail Antonio is going over there and going, 'do not do it'.
"It's causing serious issue, this is now going to damage the reputation of West Ham in Europe.
"They've been brilliant over the course of the week, the atmosphere has been jubilant - party-like - rather than aggressive.
"And then tonight, we've had a series of incidents where they have been throwing plastic cups onto the pitch and one of them now has been thrown with such velocity that it's cut the head of the Fiorentina captain."
Most read in Football
West Ham 0-0 Fiorentina LIVE: Biraghi left bleeding after object thrown, VAR saves Irons
Lionel Messi confirms he'll join David Beckham's Inter Miami to end Barcelona reunion talk
How to watch West Ham vs Fiorentina for FREE in Europa Conference League final tonight
Chelsea transfer news LIVE: Kante nears Saudi move, Colwill may be used in Caicedo deal
Alongside him was ex-Hammers star Dean Ashton, who said: "It's just disgusting to see. I don't see why they do it.
"It's been a great week, so far it's been an excellent game, really contested by the two sides.
"Declan Rice has gone over to try and console Biraghi and show that he's supporting him and he doesn't condone those actions."
There was an announcement over the tannoy from UEFA urging West Ham fans to calm down.
It was not the first time that the Italian had objects from the crowd thrown at him.
This was the third corner that Fiorentina had from the right-hand corner flag.
And every time, fans were throwing cups at the 30-year-old, though this was the first time that one connected.
After he was struck, Biraghi sarcastically applauded the fans behind the corner before he was given medical treatment.
Ashton added: "There's the odd idiot who thinks this is the right thing to do. It's horrible as a player fearing for your safety. It's just mindless. We hate to see it."
Read More on talkSPORT
Rory McIlroy told to 'f*** off' in heated PGA Tour player meeting after shock PIF merger
'I hope not' - Laura Woods is every Arsenal fan when learning about Chelsea's top target
It has been a feisty atmosphere inside the Fortuna Arena in Prague, where both sets of fans were only given around 5,000 tickets in the 20,000-capacity ground.
There had been trouble in the city before a ball had even been kicked with chairs being thrown between fans.