The 31-year-old Pole finished 1 minute and 52 seconds behind the winner, Lisa Vittozzi of Italy.
Meanwhile, Poland's Joanna Jakieła took 11th place in Östersund on Sunday, also posting her career-best World Cup result, Polish state news agency PAP reported.
Poland's Mąka said after the race: "I think this is a good start to the season. Obviously, I'm very happy with my result, but ... this is only the first World Cup stop, so there's still a lot ahead of me. I'm happy with my personal best."
Norwegian Tobias Torgersen last year took over as head coach of Poland’s women’s biathlon team to replace Adam Kołodziejczyk.
Biathlon is an Olympic winter sport that combines cross-country skiing and rifle shooting.
Source: TVP Sport, PAP