State Sen. Seth Harp said he didn't have the votes to push his legislation in the Senate Regulated Industries and Utilities Committee.
"I think there were forces there that wanted to do it in and we didn't have the numbers," the Republican from Midland said.
"I'd rather live to fight another day."
It is the third year that the Sunday sales bill has been bottled up in the Senate. A separate measure is pending in the House.
Georgia is one of only three states that ban stores from selling all alcoholic beverages on Sunday. The other two are Connecticut and Indiana.
Harp's bill would allow local communities to decide whether grocery and convenience stores should be able to sell alcohol on Sundays.
It has faced stiff opposition from religious groups who say it would sully the Sabbath. Gov. Sonny Perdue, a Christian conservative who doesn't drink, has said he doesn't like the bill.
Jim Beck, executive director of the Georgia Christian Coalition, called Harp's decision to yank the bill "a testament to family values in Georgia."
"We think it's effectively dead for this year."
But supporters say they will continue to push hard because consumers in Georgia have been clamoring for the change. Sunday is now the second busiest shopping day of the week, grocery store officials say. And stores are losing revenue when they cannot sell beer and wine.
"We will definitely be back," Kathy Kuzava, of the Georgia Food Industry Association, said. "Our customers are tired of waiting."
Supporters of Sunday sales thought the state's fiscal crisis would give the bill fresh momentum this year. Backers said allowing booze to be sold in stores on Sunday would bring in millions of dollars in additional sales tax revenue to the cash-strapped state coffers.