Nunez, 23, scored his first Premier League goal since before the World Cup to set Liverpool on course for a 2-0 win over Newcastle at St James' Park on Saturday -- a win which moves Jurgen Klopp's team up to eighth, six points behind fourth-placed Newcastle with a game in hand.
And after the victory, Liverpool manager Klopp said that the Uruguay international needs further assessment to discover the full extent of the injury.
"Nunez has hurt his shoulder and he needs further assessment," Klopp said. "We don't know any more at the moment, we will have to see, but it is painful for him."
Despite closing the gap on Newcastle to revive Liverpool's hopes of a top four finish, Klopp said it is too early to gauge whether his team have finally turned a corner this season.
"We are a step further forward," Klopp said. "Both goals were outstanding. The pass from Trent [Alexander-Arnold] for Darwin [Nunez] and from Mo [Salah] to Cody [Gakpo] [was] top class. A bit more of that would have been really great, but for today it's absolutely fine.
"When you are not in your best moment you have to fight for this, and that's what we did, we got our second win in a row. It feels great to be honest. We haven't had this for ages so it's a good day.
"We will see, we face one of the best teams in the world on Tuesday so it's difficult. But it's at Anfield so let's go.
"It's too early to say we are there again. But of course we will keep fighting and we will see."