The striker has now been withdrawn from the Republic of Ireland squad and is quarantining at home.
Government guidelines say Robinson has to self-isolate for 14 days.
But he will continue to self-test for Covid-19 during his isolation.
And with no precedent set, it is not yet known whether negative results will allow him to feature against Burnley.
Sheffield United’s John Egan, Preston North End’s Alan Browne and Bristol City’s Callum O’Dowda are also self-isolating after coming into contact with the same person with Covid-19.
Robinson’s absence would be a huge blow for Albion if he is unable to feature against Burnley on Monday.
Hal Robson-Kanu is a major doubt for the game after breaking his arm in the loss at Southampton.
While Charlie Austin and Kenneth Zohore are both out of favour at The Hawthorns and have been linked with moves away before Friday’s deadline.
Slaven Bilic has said multiple times he wants to bring in another striker before the window closes.
Huddersfield’s Karlan Grant is his number one target with Watford duo Troy Deeney and Andre Gray alternate options.
But Grant and Gray haven’t featured at all this season, while Deeney has made just one substitute appearance.
With money tight at The Hawthorns, Albion will not want to keep Austin or Zohore if they can move them on.
Cardiff and Derby are believed to be chasing Austin’s signature while Sheffield Wednesday are keen on Zohore.
But their departures could leave Bilic light up front for the Burnley game.
While Robinson has departed the Republic of Ireland squad, Albion youngster Dara O’Shea has been promoted from the under-21s for their Nations League clash against Finland tomorrow.