- 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 Largest jailbreak in Brazilian history at the Putim maximum security prison in Brazil, 345 prisoners run from the main gate. 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