So much so, one major fallout led to Ibrahimovic's transfer to Juventus.
Van der Vaart progressed through the Dutch giants' academy and made his senior debut in 2000 before Ibrahimovic joined from Malmo in his native Sweden a year later.
The duo made 68 appearances and won two Eredivisie titles together at Ajax, but a clash of egos meant they were never going to be pals.
During an international friendly in 2004 between Sweden and the Netherlands, Ibrahimovic fouled Van der Vaart before his side scored.
The Dutchman was forced off with injury and claimed the tackle had strained his ankle ligaments, as well as accusing it of being deliberate.
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"I didn't injure you on purpose and you know it," Ibrahimovic said. "If you accuse me again, I'll break both your legs and this time it'll be on purpose."
Van der Vaart has now revealed the aftermath of the incident and how it even caused his teammate to change clubs.
He joined talkSPORT's 'The Lineup' in partnership with BETMGM on YouTube and was asked what Ibrahimovic was really like.
"A**hole," Van der Vaart said. "We had big fights. Not a 'fight' fight but we couldn't get along.
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"He was really arrogant in my point of view, I had a big ego, we were both young. We had to play together, that was manageable but there came a point that we had a national game against Sweden and he kicked me on the ankle.
"It was really bad, you can see it on YouTube, and I was lying there, crying almost and I looked at him, and he was my teammate at Ajax. He was just walking away and was like [expression as if Ibrahimovic gestured 'what?'].
"After the game, I went mad in the presser, I said he did it on purpose, and I came in the dressing room and I thought, 'Oh s***, don't say it.' So I called him, I said, 'Listen, I'm sorry I said that in the press,' and then that was totally OK.'
"The next day of training, we had like a big round bit, the whole team, big [manager Ronald] Koeman and then all of a sudden, I thought it was OK and then he went [bang] totally on me, screaming.
"I screamed back, some part of the team choose him, some part my side, and then two days later he left for Juventus because I had to leave or he [did]."
Neither wanted to play with the other anymore.
"But he was lucky that Juventus wanted to [sign him] and I was lucky that I could stay for my dream club," Van der Vaart added.
Ibrahimovic signed for Juventus from Ajax in August 2004 for £13.3million, scoring 26 goals in 92 appearances for the club.
He later played for clubs including Inter Milan, Barcelona, AC Milan, Paris Saint-Germain and Manchester United before retiring in 2023 having won a multitude of major honours.
When asked if he spoke to Ibrahimovic again, Van der Vaart said: "After that we played two times [against each other] but now we are totally OK.
"Also he wrote something in his book about it, this story was really big in Holland, there became jokes about it."
He later added: "I really hope that I can see him again because I have so much respect for him.
"We laugh about it because I also made really big mistakes, he did, Koeman did, we were all young. Big ego, young, you think you're the best in the world, I was thinking I was the best."
Van der Vaart left his boyhood club Ajax in 2005 for Hamburg, with later spells coming at Real Madrid, Tottenham, Real Betis and Danish sides FC Midtjylland and Esbjerg fB.
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The attacking midfielder was also part of the Netherlands side that reached the final of the 2010 World Cup.
Watch the latest episode of The Lineup in full on talkSPORT's YouTube channel at 4pm in partnership with BETMGM!