Striker Michu will be sidelined for a month with the ankle injury he suffered in the 1-0 defeat by Cardiff on Sunday.
He was expected to miss Swansea's next two games, against Russia's Kuban Krasnodar and Stoke City in the league, but will now be out for longer.
Manager Michael Laudrup confirmed Michu's injury is worse than originally thought.
"He hasn't been 100% and now he is out again for maybe three or four weeks," said Laudrup.
"He is our top scorer for last year and he has been struggling for the last two, three or four weeks.
"He has also been struggling with his knees for many weeks, but he wanted to play anyway.
"He is one of our important players, and knows with the ankle injury he can get his knees solved as well."
Swansea face Kuban Krasnodar in Group A of the Europa League on Thursday and a win would take them closer to securing a place in the knockout stages.
Left-back Ben Davies has been passed fit for the game in Russia, having missed Swansea's previous three games with an ankle injury.
But Pablo Hernandez is out after suffering a torn thigh muscle while defender Garry Monk is still sidelined with a knee problem.