"The last few weeks have been different.
But I'm able to say weeks and not months because of great medical help, a little luck and a good decision," Svindal said on Instagram.
He added that the cancer was caught early and the prognosis looked very good.
The skier struck gold in the super-G at the 2010 Vancouver Games and in the downhill eight years later in Pyeongchang. He also owns five world championship golds.