The 17 year-old was a second-half substitute as Denmark drew 3-3 with Poland in Turkey on Thursday. Obi played the final 15 minutes of the tie.
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Obi and Denmark are next in action on Monday against Italy.
The youngster has turned out for England at U16 level, though now appears committed to Denmark, where he was born and raised.
Obi has now made four Premier League appearances for United's first team this season.