The French goalkeeper will definitely miss the round of 32 first leg meeting in Florence as well as Sunday’s FA Cup fifth-round tie at home to Crystal Palace.
And while Spurs head coach Mauricio Pochettino has backed under-study Michel Vorm to step up to the mark, he admits not having his skipper available will have an effect.
“It is not a big, big issue,” he said last night in Florence.
“It is a very small injury. It will always impact, Hugo is our captain and it is a very important period for us but how it is important, we know now we have a squad and we believe that Michel is a very good, top goalkeeper too, and we believe in him and trust in him.
“It is true it is a big impact but in one week we expect and hope he is available to start to play again.”
Lloris picked up the injury turning away a Sergio Aguero cross deep into the 2-1 win at City on Sunday, which left Tottenham second in the Premier League.
“The last action of the game against Manchester City, Hugo hurt his shoulder and he is out for tomorrow and for Sunday too,” Pochettino explained.
“We need to assess him during the week if he can be available for next Thursday but for sure, tomorrow and next Sunday he is out.”
With a Premier League title tilt in full swing, Tottenham could be forgiven for taking an eye off their Europa League campaign - much like when they were knocked out by Fiorentina at the same stage last year.
Then, they were just three days from a Capital One Cup final clash with Chelsea, but this time around Pochettino insists he will maintain his stance on wanting to win in Europe.
““I can understand, because our position in the table it is a very big opportunity to fight for the Premier League but, for me, when you’re in a big club like Tottenham you need to fight in every competition and every game.
“I don’t think too much into the future. The most important game is tomorrow and the Premier League can wait for a few weeks. When you manage Tottenham, you need to try and win every competition and every game.”
Fiorentina head coach Paulo Sousa expecting a different challenge from Tottenham compared to last year, when the Viola won 2-0 in Florence, winning 3-1 on aggregate.
“It’s a different Tottenham from last year,” Sousa said.
“Players have come into their squad who are giving more and they’ve managed to rotate throughout the season while maintaining very high levels, and that’s important.
“They have a lot of quality, so even an injury doesn’t make them weaker. They’re more consistent and in fact they have more points.”