The pair were missing from the matchday squad against Jose Mourinho’s men when it was released earlier on Sunday.
'They did a test on Monday and unfortunately it was positive so they have to be for 10 days in self-isolation. We cannot do anything about it. It doesn't change the way we approach the game,' Bilic told Sky Sports.
A West Brom club statement read: 'Slaven Bilic has confirmed two Albion players will miss today's Premier League fixture against Tottenham Hotspur after testing positive for COVID-19.
'Branislav Ivanovic and Matheus Pereira have begun a period of self-isolation.
'The club wishes the players a speedy recovery and will support them, if necessary, during their quarantine.'
Former Chelsea defender Ivanovic joined West Brom on a free transfer this summer after leaving Russian side Zenit Saint Petersburg. The 36-year-old Serbian defender has featured three times in the Premier League so far this season.
Pereira, who spent last season on loan at the club from Sporting Lisbon before making a permanent move this season, has scored once in seven Premier League games thus far.
West Brom are one of three clubs including Burnley and Sheffield United who are winless in the top flight this season.
