"I informed Reuven today of his dismissal as coach. It is the most difficult decision I have had to make in my 20 years as owner," Yaakov Shahar told the club's website.
Atar, 43, was appointed towards the end of last season when it became clear his predecessor Elisha Levy would not continue for a fifth campaign.
Haifa have been one of Israel's most successful clubs over the past three decades during which they have won all their 12 league titles but last season was disappointing.
They have also been one of the country's best teams in European competition but they missed out last season after finishing fifth in the 14-team Premier League.