The 23-year-old pulled a hamstring during last week's 0-0 draw with Chelsea.
It was initially thought that Walcott could be facing a long spell on the sidelines, but Arsene Wenger has now revealed that the winger could be fit in time for the Gunners' final game of the season.
"It is less serious than we thought," said Wenger. "He has a small chance to play in the last game. He won't play against Norwich but for the Euros, there is no doubt.
"For the Euros, he is definitely available. It is minor - not as big as we thought it was. I think in fact the injury of Walcott is good news for England because he just has a little rest."
Walcott, who has 22 international caps, has made 39 appearances for Arsenal this season, scoring nine goals.