Jonk started his career in amateur club RKAV Volendam, before signing for Volendam in 1986. As a central midfield player, he scored many goals, assisting his club to promotion to the Eredivisie in 1987, where he scored a further of five goals. Ajax monitored his progress keenly and his skills did not escape the scouts of the club, who hastened his transfer to Amsterdam in 1988.
At Ajax, he slotted into the squad easily, even scoring 6 goals in his debut season. First team chances were regular, if not abundant, but his first appearance for the Dutch national team seemed a long way away. His gameplay is not very artistic, but he has earned a reputation as a midfield anchor in the same mould as other Dutch players like Aron Winter, Erwin Koeman, Philip Cocu and Mark van Bommel. Therefore, with the Dutch 1990 World Cup squad brimming with attack-minded midfielders like Richard Witschge and Jan Wouters, he was unsurprisingly omitted from selection for the national team in the late 1980s as well as the 1990 World Cup squad. He helped Ajax to the 1992 UEFA Cup Final in which he scored to help them overcome Torino.
His pin-point passing, outstanding vision and combative and hard-working style of play earned him his debut for the Dutch national team in a 3 - 2 win in a friendly against Austria on 27 May 1992 and he signed on for Internazionale in 1993 before the 1994 World Cup, where he was joined by compatriot Dennis Bergkamp. The Italian club had seemingly followed their illustrious city rivals Milan into buying Dutch players in the hope to emulate Milan's success with Marco van Basten, Frank Rijkaard and Ruud Gullit in the late 1980s and early 1990s.
The Dutch 1994 World Cup squad selected by then coach Dick Advocaat had been tipped to reach the quarter-finals of the tournament and Advocaat had opted for a central midfield pairing of Jonk and usually Jan Wouters or Rob Witschge, supported by speedy wingers such as Marc Overmars and Bryan Roy. In the first group game against Saudi Arabia, the Netherlands fell behind to a goal by Saudi player Fuad Amin in the 19th minute of the match before Jonk opened his World Cup scoring account by netting a 50th minute long-range effort from a good 35 metres out. Though the keeper could have saved the shot, it went in nonetheless, and the goal became one of the most spectacular of the tournament.
The Dutch went on to win the match by a goal from Gaston Taument in the 86th minute. Jonk would score another goal against the Republic of Ireland from another long-range effort and a goalkeeping blunder, in a convincing 2 - 0 win to help the Dutch qualify for a quarter-final meeting with Brazil.
Meanwhile, at Internazionale, he managed 54 appearances in two seasons and scored eight goals. He scored in a UEFA Cup Final again, this time as Internazionale won the 1994 final. However, when fellow team-mate Dennis Bergkamp left Internazionale for Arsenal at the end of the 1994 - 95 season, he felt that opportunities for a first team place at the Italian club seemed to be under threat (he was by then close to being 30 years old) and he went back to the Netherlands to sign with PSV. He stayed long enough at PSV to convince then manager Guus Hiddink to be selected for the 1998 World Cup in France, after being overlooked for Euro 1996. At the 1998 World Cup, Jonk played in five of the seven matches that the Netherlands played and did not score any goals.
With the appointment of Frank Rijkaard as the new manager after the 1998 World Cup, Jonk's international career seemed to be over. However, he did play once more for the Netherlands in a friendly against Denmark on 18 August 1999. Jonk finished his international career on 49 caps and 11 goals.
For the 1998 - 99 season, Jonk went to join Sheffield Wednesday for a fee of £2.5 million, where he was a regular starter for the relegation-threatened side. Apparently, his once-impressive performances for both club and country had gone and he was frequently injured, which caused the Wednesday fans to voice dissent about a clause in his contract which stipulated that he would automatically receive £5,000 per game which he would miss through injury. At the beginning of the 2000 - 01 season, he announced his retirement from the game.