Jerome Champagne, FIFA deputy general secretary in charge of political issues, said on Friday the attack was a direct strike without any reason.
He said the field was not being used by Palestinians as a missile launching pad, as Israel's ambassador to Switzerland had claimed.
"We have just asked for explanations," Champagne said.
"FIFA has been fighting for more than a century to make this game universal. To hit a football field is really the wrong signal."
"Football should remain outside of politics"
Champagne said he had discussed the matter with Sepp Blatter, the FIFA president, and that a decision would likely be announced early next week.
He declined to elaborate on what action FIFA could take against Israel.
"Football should remain outside of politics," Champagne said.