The Everton defender picked up his problem in the 3-3 draw at Sligo Rovers last week and although he was in the stand for yesterday's defeat at Salford City, he didn't make it onto the bench.
Tarkowski has been an ever-present since he joined the Toffees and played every minute of the Premier League campaign last season.
He has become renowned as an immensely resilient player and a teak-tough centre-back who is hugely reliable and consistent.
Were Everton to lose the 31-year-old former Burnley stalwart for any length of time it would be a major blow.
While it seems that the Blues will succeed in keeping Jarrad Branthwaite at least for another year - although he has not signed a new contract which is allegedly being offered - Tarkowski is arguably just as important to the team's defence.
And with Ben Godfrey having left for Atalanta and Mason Holgate a player Sean Dyche is unlikely to give much playing time to after being on loan last season (and potentially leaving again if an offer comes in for him) Micheal Keane is the only other centre-back in the squad.
Unfortunately, we all know how unreliable Keane is and few Evertonians will want to see the team having to turn to him for any length of time.
Jake O'Brien is a player the Blues have been heavily linked with on several occasions already this summer and those stories are continuing.
The 23-year-old Irishman is a player on the radar of several clubs after an excellent campaign with Lyon last season.
He is a central defender who looks a very good fit for Everton given his age and qualities and so a move for him makes a lot of sense.
However, despite having signed several forwards, Everton are it seems still interested in further options upfront with reports that the club are continuing to pursue Wilfred Gnonto for example.
So, given the financial constraints they are under, it will be interesting to see whether the Toffees will be able to secure a deal for the player who might cost near to £30 million, but it is clear that the squad needs reinforcement in this position.
With Dyche's preferred formation and tactics placing such a huge emphasis on a very strong, solid and consistent defence, the Toffees will certainly need enough depth at centre-back to get though the upcoming campaign.