- Jun 6 In Australian Rules Football, Tony Lockett breaks the record for career goals, previously 1299 by Gordon Coventry and which had stood since 1937.
- Jun 6 At the Putim maximum security prison in Brazil, 345 prisoners run from the main gate in the largest jailbreak in Brazilian history, marking the 10th escape for the three-year-old facility. In the ensuing manhunt, two fugitives are killed and five innocent bystanders are accidentally jailed.
- Jun 6 53rd Tony Awards: Fosse & Side Man win
- Jun 9 Kosovo War: the Federal Republic of Yugoslavia and North Atlantic Treaty Organization sign a peace treaty.
Jun 10 Kosovo War: NATO suspends its air strikes after Slobodan Milošević agrees to withdraw Serbian forces from Kosovo.
- Jun 22 Former Mpumalanga premier, Ndaweni Mahlangu causes a storm within political circles with his now infamous statement, "It is acceptable for politicians to lie", South Africa
- Jun 25 In his first state of the nation address, South African President Thabo Mbeki promises to tackle rampaging crime; the nation's murder rate is the third highest in the world and more than 49,000 cases of rape were reported in 1998
- Jun 27 ATB go to No.1 on the UK singles chart with '9pm, Till I Come'
- Jun 27 The Chemical Brothers go to No.1 on the UK album chart with 'Surrender', their second No.1 album
- Jun 26 Bestselling novelist Tom Clancy (52) weds freelance journalist Alexandra Llewellyn (32) in Manhattan