Pandya was included in India's Test squad for their home series against England in late 2016, but was eventually left out after he injured himself while training in the nets at the PCA Stadium. He was named in the squad that toured Sri Lanka in July 2017 and played his first Test on 26 July in Galle. In the 3rd and the final Test match against Sri Lanka at Pallekele, Pandya scored his maiden Test century, and set the record for becoming the first Indian batsman to score a Test century just before lunch. He also set the record for scoring the most runs in a single over of a Test innings for India, scoring 26 runs, which was later surpassed by Jasprit Bumrah. This century was his first century in international cricket.

Pandya's brother Krunal has also played for India and the Mumbai Indians. Their father, Himanshu Pandya died in January 2021 of cardiac arrest.

Pandya got engaged to dancer and actress Nataša Stanković on 1 January 2020; on 30 July 2020 their first child, a boy, Agastya Pandya was born. On 14 February 2023, the couple renewed their wedding vows in a ceremony in Udaipur, Rajasthan. In 2024, the couple's relationship came under scrutiny during Pandya's maiden season as captain of the Mumbai Indians, as Stanković took down their posts together and took his last name out of her username on Instagram. The couple mutually separated in July 2024.

In January 2019, Pandya appeared with teammate K. L. Rahul on the show Koffee with Karan, and made several controversial comments which were met with immediate public backlash. During the interview, Pandya spoke about how he had proudly informed his parents of his first sexual encounter, which was well received by them. He also proclaimed that he likes to "observe how women move" at high-end bars and nightclubs, as well as on social media and then went on to liken himself to a black person saying, "I'm a little from the black side so I need to see how they move". The public categorized his monologue as indecent, derogatory, misogynistic and disgraceful. Pandya apologized for his remarks by saying that he had gotten carried away by the nature of the show. The Board of Control for Cricket in India (BCCI) responded to the controversy by saying, "It will be considered whether players should even be allowed to appear on such TV shows which have got nothing to do with cricket." The BCCI found the comments as very crass, sexist and cringeworthy, and was not impressed by the apology, seeking appropriate legal action into the matter as it was a breach of conduct. Both Pandya and Rahul were handed a suspension until a pending investigation and were called back from the ongoing tours of Australia and New Zealand. Furthermore, on 13 January 2019, Gillette suspended their brand association with Pandya for its Mach3 razor. On 24 January 2019, after lifting the suspension on Pandya and Rahul, the BCCI announced that Pandya would re-join the squad for the matches in New Zealand.