"The batsman had struck hard. The fast ball first hit the stumps, got deflected and hit Awaskar on his neck yesterday. He collapsed on the ground," one of the players, Yona, told PTI.
55-year-old Awaskar, who originally hailed from Mumbai, was evacuated to a hospital in a critical condition, where medics were unable to revive him.
Israeli newspaper Haaretz quoted doctors who tried to resuscitate Awaskar as saying that he suffered a heart attack after being hit by the ball.
The Israeli police has ruled out any foul play in the incident but is still investigating the case.
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Awaskar has been among leading performers for the Israel national cricket team during his youth and continued to be actively involved in the game by later picking up umpiring and even officiating in the European Cricket league games.
The Israel Cricket Association CEO, Naor Gudker, who also happens to be an international umpire, told PTI that it was the last game of the league season between Lions Lod and Young Ashdod.
"The cricket fraternity in Israel is in a shock. We are all like a family and it is a loss for all of us," he said. "This is a tragedy for his family and for cricket in Israel."
His last matches for Israel were in division two of the European Championships in 2006.
A left-arm spinner and hard-hitting top-order batsman, he had the local league record for the highest score, 244 not out, scored for the Ashdod A side, local media reports said.
Awaskar was married with two daughters.
Teams participating in the winter league in Israel have decided to postpone the scheduled matches next week with condolence messages pouring in from all over Israel.
Cricket is not a very popular sport in Israel, though there is an amateur league comprising players from India and countries like South Africa, Australia and New Zealand.