The Agence France Presse says the PCB has asked national president Mohammad Rafiq Tarar to set up a formal investigation into defeats by Bangladesh and India during the tournament in England.
The news comes just a week before England are due to arrive in Pakistan for their first tour since 1987.
Pakistan lost by 62 runs to Bangladesh in a first round match at Northampton, the only win their opponents have ever achieved against a Test-playing nation.
Pakistan then went down by 47 runs against India during the Super Sixes phase of the tournament, but still went on to reach the final where they lost to Australia.
"PCB chairman General Tauqir Zia has requested the president to order a judicial inquiry into the allegations of betting, match fixing and gambling concerning the World Cup 1999 matches against Indian and Bangladesh," a Board statement read.
Dr Ali Bacher, the managing director of the United Cricket Board of South Africa, told the King Commission in Cape Town earlier this year that former PCB chief executive Majid Khan had told him two of Pakistan's World Cup games had been fixed.
Khan later supported Bacher's evidence, but said he had no proof of the allegations.
The inquiry call is believed to have been prompted by the International Cricket Council, whose own match-fixing probe is being headed by former Metropolitan Police commissioner, Sir Paul Condon.
The Board said that allegations concerning Javed Akhtar's umpiring during the England v South Africa Test at Headingley in 1998 should also form part of the inquiry.
Akhtar gave nine of the 10 lbw decisions during the game, eight of them against South Africa, but has insisted the claims are "baseless".
Pakistan cricket has already been subject to one match-fixing inquiry conducted by Justice Malik Qayyum.
His report called for life bans for former captain Salim Malik and fast bowler Ata-ur-Rehman and fines for current players Wasim Akram, Mushtaq Ahmed, Saeed Anwar, Mushtaq Ahmed and Akram Raza.
His investigation focused on the period between September 1998 to October 1999, but did not look into allegations concerning the World Cup.