In 2012 Banušić scored 16 goals for Norrettan club IK Sirius and became a transfer target for clubs in the Damallsvenskan, Sweden's top division.[3] Banušić made a favourable early impression after signing for Kristianstads in 2013. Teammate and fellow Uppsala-native Josefine Öqvist called her a potential "världsspelare" (English: world-class player), while coachElísabet Gunnarsdóttir declared her the biggest talent in the history of Swedish women's football.[4]
Banušić gave Kristianstads the lead in the 2014 Svenska Cupen (English: Swedish Cup) final, but they were defeated 2–1 by Linköpings FC.[5] After the season she decided to leave Kristianstads and returned to Uppsala, where she considered several offers from other clubs from Sweden and abroad.[6] Banušić agreed a transfer to London-based FA WSL club Chelsea Ladies in January 2015.[7]
With Chelsea Banušić started three of her eight league appearances as the club won the 2015 FA WSL title. She was an unused substitute in Chelsea's 1–0 win over Notts County at the 2015 FA Women's Cup Final, staged at Wembley Stadium for the first time. Banušić had fallen further down the pecking order when Chelsea broke the British transfer record to sign Fran Kirby during the season.
In December 2015 Banušić announced that she would return to Sweden to play for Damallsvenskan club Eskilstuna United DFF in 2016.[8] After moving to Linköpings FC the following season, her new club won the 2017 Damallsvenskan title. While her teammates celebrated, an emotional Banušić invited her critics to eat their words.[9] In July 2018 she was reunited with her former Linköping coach Kim Björkegren when she transferred to the Chinese Women's Super League club Beijing Phoenix.[10]
On 1 February 2021, Banušić signed with Italian Serie A team Roma.[11] She made her Roma debut on 6 February 2021, coming off the substitutes' bench in Roma's 4–0 away victory over Pink Bari.[12] In her third appearance for Roma, Banušić scored an overhead kick against Inter Milan in what would prove to be the winning goal on the day.[13] Banušić was also part of the Roma squad that won the 2021 Coppa Italia final against AC Milan in May 2021.[14]
In total, Banušić made five appearances for Roma and scored one goal during her half-year stay in the Italian capital. On 14 July 2021, it was announced that Banušić had moved from Roma to newly-promoted Serie A club Pomigliano.[15] Seven goals in 21 appearances helped Pomigliano avoid relegation, before Banušić signed for Parma in July 2022.[16]
On 2 August 2023 she signed for newly-promoted Serie A club Napoli.[17]
In November 2014 Banušić made her senior Sweden debut against Canada in Los Angeles. The match, which finished in a 1–0 defeat, was played behind closed doors but still counted as a full FIFA international fixture. Banušić was disappointed with the result but satisfied with her performance after coming on as a second-half substitute. She hoped to stay in contention for a place at the 2015 FIFA Women's World Cup.[20] She was particularly disappointed to be dropped from the national team for UEFA Women's Euro 2017, although she was recalled shortly afterwards.[2]
Because of her Croatian origin,[2] she was also eligible to represent Croatia.