their 23–18 victory over the in the semi-final and the final, where his side could not emulate their 2014 result, losing 24–32 to the . Kleyn suffered an arm injury in a warm-up match against the prior to the 2016 Super Rugby season, which ruled him out of the start of the competition. During the international break, Kleyn started two matches for Western Province in the 2016 Currie Cup qualification series, the first of those being a match against the during which Kleyn scored his first try in senior rugby, scoring ten minutes from time to help his side to a 43–34 victory. He was included in the Stormers touring squad for their trip to Australia to face the and the , but failed to be included in their matchday squad. He eventually made his only appearance of the season in their 52–24 victory over the in their final match of the regular season. Munster Kleyn secured an early release from his contract with in July 2016, leaving South Africa to join Irish United Rugby Championship side Munster on a three-year contract prior to the 2016–17 Pro12 season. On 3 September 2016, Kleyn made his competitive debut for Munster when he came on as a substitute against Scarlets in the sides opening 2016–17 Pro12 fixture. On 17 September 2016, Kleyn scored his first try for Munster in their 20–16 away win against Welsh side Dragons in Rodney Parade. The match was also his first start for the province. On 17 February 2017, it was announced that Kleyn had been ruled out for 8–10 weeks due to a neck injury. The injury was sustained during the United Rugby Championship fixture against Dragons on 10 February. On 1 September 2017, in what was his return to competitive action following the aforementioned neck injury, Kleyn scored two tries in Munster's win against Benetton in Round 1 of the 2017–18 Pro14. Kleyn scored a try and won the Man-of-the-Match award in Munster's 21–16 win against Ospreys on 16 September 2017. Kleyn was nominated for the 2018 Munster Rugby Player of the Year award in April 2018. He signed a three-year contract extension with Munster in September 2018. Kleyn was ruled out for six weeks after undergoing surgery for a thumb injury in November 2018. He returned from the injury in Munster's Pro14 fixture against Ulster on 21 December 2018. Kleyn earned his 50th cap