Prithvi joined an elite group of Indian batters by scoring a century on his Test debut in October, 2018. However, he has struggled to secure a consistent place in the team, playing only 5 Tests, 6 ODIs, and 1 T20I. The Mumbai opener has frequently made headlines for the wrong reasons.

Shaw became embroiled in a social media controversy when he was accused of assault by social media influencer Sapna Gill. The incident reportedly occurred in a Mumbai nightclub after Shaw allegedly refused to take a selfie with her. Things escalated when the influencer and her friends allegedly attacked Shaw's car with a baseball bat, prompting his friend to file a police complaint. The incident quickly became a media sensation, with both sides accusing each other of wrongdoing, while Shaw claimed he was being harassed.

Ahead of the 2022 IPL season, the NCA mandated all centrally contracted players to undergo a Yo-Yo fitness test, regardless of their health or injury status. Shaw, contracted with the Delhi Capitals, attended the NCA despite not being a BCCI-contracted player. He participated in the fitness test but did not receive clearance, scoring below 15 in the Yo-Yo test, while the minimum cutoff for male cricketers was set at 16.5 in 2022. The news quickly gained traction in mainstream media, with many raising concerns about his commitment to personal fitness.

During the 2019 Syed Mushtaq Ali Trophy, Shaw's samples were collected as part of the BCCI's anti-doping procedures. His sample tested positive for terbutaline, a substance banned by WADA. Consequently, the board imposed an 8-month ban on Shaw for violating doping regulations, causing him to miss the first half of the 2018-19 domestic season

In response to widespread criticism, Shaw also went on to state that he accidentally consumed a cough syrup containing terbutaline. He accepted responsibility and acknowledged that, as a professional cricketer, he should have been more mindful of what he consumes.

Shaw found himself embroiled in yet another controversy when his photo with model-actress Nidhi Tapadia went viral on social media. The accompanying text on the Instagram Stories read, 'Happy Valentine’s my wifey', followed by emojis. Later, the cricketer, however, clarified: 'Someone editing my pics and showing stuff that I haven’t put on my story or on my page. So, ignore all the tags and messages. Thanks.'

Shaw made headlines again when police detained and questioned him for violating lockdown regulations during a vacation in Goa back in 2021. He reportedly was unaware of the restrictions imposed by the Maharashtra government, as he left the state for Goa without obtaining an e-pass.

Shaw last played a Test for India during the 2020-21 tour of Australia, participating in the opening match at the Adelaide Oval, where India was bowled out for 36 and suffered an eight-wicket defeat. Between 2018 and 2021, he represented India in five Tests, six ODIs, and one T20I.