The 32-year-old picked up a thigh problem in Saturday's 1-1 draw with Norway in Oslo.
The Bayern Munich forward will now undergo a scan on Monday to determine the extent of the problem.
"I cannot guarantee that Olic will play at the Euros," said Croatia squad doctor Zoran Bahtijarevic.
Slaven Bilic's side start their campaign against the Republic of Ireland on Sunday, June 10.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 7 | 6 | 0 | 1 | 13 | 2 | 11 | 18 |
| 2 | Manchester CityMan City | 6 | 4 | 2 | 0 | 14 | 6 | 8 | 14 |
| 3 | Arsenal | 6 | 4 | 2 | 0 | 12 | 5 | 7 | 14 |
| 4 | Chelsea | 6 | 4 | 1 | 1 | 15 | 7 | 8 | 13 |
| 5 | Aston Villa | 6 | 4 | 1 | 1 | 12 | 9 | 3 | 13 |
| 6 | Fulham | 6 | 3 | 2 | 1 | 8 | 5 | 3 | 11 |
| 7 | Newcastle UnitedNewcastle | 6 | 3 | 2 | 1 | 8 | 7 | 1 | 11 |
| 8 | Tottenham HotspurSpurs | 6 | 3 | 1 | 2 | 12 | 5 | 7 | 10 |
| 9 | Brighton & Hove AlbionBrighton | 6 | 2 | 3 | 1 | 10 | 8 | 2 | 9 |
| 10 | Nottingham ForestNott'm Forest | 6 | 2 | 3 | 1 | 6 | 5 | 1 | 9 |
| 11 | Bournemouth | 6 | 2 | 2 | 2 | 8 | 9 | -1 | 8 |
| 12 | Brentford | 6 | 2 | 1 | 3 | 8 | 10 | -2 | 7 |
| 13 | Manchester UnitedMan Utd | 6 | 2 | 1 | 3 | 5 | 8 | -3 | 7 |
| 14 | West Ham UnitedWest Ham | 6 | 1 | 2 | 3 | 6 | 10 | -4 | 5 |
| 15 | Ipswich TownIpswich | 6 | 0 | 4 | 2 | 5 | 10 | -5 | 4 |
| 16 | Everton | 6 | 1 | 1 | 4 | 7 | 15 | -8 | 4 |
| 17 | Leicester CityLeicester | 6 | 0 | 3 | 3 | 8 | 12 | -4 | 3 |
| 18 | Crystal Palace | 7 | 0 | 3 | 4 | 5 | 10 | -5 | 3 |
| 19 | Southampton | 6 | 0 | 1 | 5 | 3 | 12 | -9 | 1 |
| 20 | Wolverhampton WanderersWolves | 6 | 0 | 1 | 5 | 6 | 16 | -10 | 1 |
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