Jasna is located about 95 miles from Krakow.
Neither country has hosted the Winter Olympics. Zakopane bid unsuccessfully for the 2006 Winter Games, while the Slovak resort of Poprad-Tatry failed in attempts for the 2002 and 2006 Games.
The Poland-Slovakia joint bid is the fifth declared candidacy for the 2022 Games.
The Norwegian capital of Oslo, which last hosted the Winter Games in Lillehammer in 1994, announced its bid earlier Thursday.
Oslo's bid includes plans to hold the medal ceremonies in the city center and several competitions in venues on the city outskirts. The Alpine events would be held in Lillehammer, about 85 miles north of Oslo. The venues for the opening and closing ceremonies have not yet been decided, Olsen said.
In May, the Oslo city council voted in favor of asking for a $5.7 billion financial guarantee from the Norwegian government a precondition for hosting the games. Norwegian lawmakers are expected to decide on that in the second half of 2014, Olsen said.
A popular referendum in Oslo in September backed the bid to host the games.
Nov. 14 is the deadline for submission of bids to the International Olympic Committee.
The field also includes the Ukrainian city of Lviv; Beijing and the northern Chinese city of Zhangjiakou; and Almaty, Kazakhstan. A referendum will be held Sunday in Germany on a proposed bid from Munich.
The IOC will select the 2022 host city in 2015. Oslo, Norway
Associated Press writer Jan M. Olsen in Copenhagen, Denmark, contributed to this report.