Domestic and T20 Career

In August 2017, Klaasen was named in the Nelson Mandela Bay Stars squad for the inaugural T20 Global League season. However, in October 2017, Cricket South Africa initially postponed the tournament until November 2018, after which it was canceled shortly afterwards.

On April 2, 2018, Klaasen moved to Indian Premier League club Rajasthan Royals, replacing Steve Smith.

In June 2018, Klaasen was named to the Titans team's squad for the 2018–19 season. In October 2018, he was named in the Durban Heat squad for the inaugural edition of the Mzansi Super League T20 tournament.

In December 2018, Klaasen was purchased by Royal Challengers Bangalore as part of the player auction for the 2019 Indian Premier League. In June 2019, he was selected to play for the Toronto Nationals franchise team in the 2019 Global T20 Canada tournament. In July 2019, he was selected to play for the Glasgow Giants in the first edition of the Euro T20 Slam cricket tournament. However, the following month the tournament was canceled.
In September 2019, Klaasen was named in the Tshwane Spartans team's squad for the 2019 Mzansi Super League tournament. He was released by Royal Challengers Bangalore ahead of the 2020 IPL auction.

Shukri Conrad, coach at Cricket South Africa's National Academy, said Klaasen could become the South African equivalent of MS Dhoni. In September 2015 he said: “Heinrich remains very calm about the situation. He stays in the moment. He has a lot of a poor man's MS Dhoni about him. He really has no sideshows in his game and really takes the game to the top.” Opponents. He doesn't wait for the game to come to him and that's what I like most about him. He’s as tough as they come.”

In April 2021, Klaasen was called up to the Northerns squad ahead of the 2021–22 South Africa cricket season.

He was bought by Sunrisers Hyderabad to play in the Indian Premier League in 2023.

In February 2023, Klaasen scored the second century in the SA20 tournament, scoring 104 from 44 balls for Durbans Super Giants against Pretoria Capitals. He also made his maiden IPL century against former team Bangalore in May 2023, scoring 104 runs off 51 balls.

In July 2023, Klaassen became the first player in Major League Cricket to score a century, playing for the Seattle Orcas against MI New York, scoring 110 runs off 44 balls.

International Career

In February 2017, Klaasen was called up to South Africa's Test squad for the series against New Zealand, but did not play.

In February 2018, Klaasen was included in South Africa's One Day International (ODI) squad for the series against India, replacing the injured Quinton de Kock. He made his ODI debut on February 7, 2018 against India. In his second ODI, in the fourth ODI of the home series against India, he won his first international Man of the Match award with 43 runs off 27 balls.

In the same month, Klaasen was named in the South Africa Twenty20 International (T20I) squad, including for the series against India. He made his T20I debut for South Africa on February 18, 2018 against India. On 21 February, Klaasen scored his first T20I fifty in the second T20I match against India, which South Africa won by 6 wickets, and was also named man of the match for scoring 69 runs in 30 balls, including 3 fours and 7 sixes.

In February 2018, Klaasen was called up to South Africa's Test squad for the series against Australia, but did not play. In August 2019, he was included in South Africa's Test squad for the series against India, replacing the injured Rudi Second. He made his Test debut for South Africa on October 19, 2019 against India. On 29 February 2020, Klaasen scored his first century in an ODI match, scoring an unbeaten 123 against Australia.

In January 2021, Klaasen was named captain of the South African T20I squad for the away series against Pakistan. In April 2021, Klaasen was again named South Africa's T20I captain, this time for the home series against Pakistan, after Temba Bavuma was ruled out due to injury. In September 2021, Klaasen was named in the South African squad for the 2021 ICC Men's T20 World Cup.