The 30-year-old Polish player, ranked world No. 45 by the Women's Tennis Association (WTA), lost to the fifth-seeded Belarusian in straight sets, 6-7, 2-6, in Melbourne on Thursday.
It was the first time Linette had played for a place in the Australian Open final, posting her best Grand Slam result and hitting a career milestone.
Linette was the last Pole standing in the singles at this year's Australian Open, which runs until Sunday.
Poland's world No. 1 Iga Świątek crashed out of the tournament in the fourth round, after being eliminated by Elena Rybakina of Kazakhstan in the women's singles.
On the men's side, Poland’s Hubert Hurkacz was ousted by American Sebastian Korda in the fourth round.
Meanwhile, Polish player Jan Zieliński has moved into the final of the men’s doubles in Melbourne, partnering with Hugo Nys of Monaco.
Zieliński and Nys will face home favourites Jason Kubler and Rinky Hijikata in the championship match at Melbourne Park on Saturday.
Source: IAR, PAP, Eurosport