A leading orthopaedic surgeon claims Kane will be out for six months.
England will play Austria in Vienna and Romania at a home venue to be confirmed in June.
England will face Croatia, Czech Republic and potentially Scotland in Group D of Euro 2020.
The draw, conducted in Nyon on Friday, paired Steve Clarke's side with the nation that finished fifth in Group G.
Monday night's 1-1 draw at the Aviva Stadium means it is the Danes who progress automatically along with Switzerland.
Harry Kane became the first England player to score in every round of a qualifying campaign as Kosovo were beaten 4-0.
What did we learn from England? Well, nothing we didn't already know. Southgate's search for answers goes on...
England were sloppy at the back but played some excellent attacking football in a ridiculously open game at St. Mary's.
Southgate believes his team can help to give the nation a feel-good factor amid an uncertain political backdrop.
David McGoldrick snatched a priceless Euro 2020 qualifier draw with his first international goal.
Gareth Southgate knows England need to keep raising the bar if they are to have a shot at Euro 2020 glory.
While the expansion of the Euros horrifies some, FC Gabala owner Tale Heydarov is feeling optimistic...
Another goal and an assist for the City man, while Ross Barkley also shone.
And did the Nations League have any bearing at all? Could England be drawn against Germany? Yes and yes.
The best thing about this list? No sign of Jake Livermore. So what does the future hold for England?
England aren't going to win the 2018 World Cup after all, but there are other things to win...
Jack Grealish and Harry Winks are bringing it home in two years' time. And was Keano right?
Expect more of the same at Euro 2020. UEFA insist there is no problem with the 24-team format.
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