Team founder and co-owner Dale Earnhardt Jr. issued a statement saying Eury was "no longer with the company" after Patrick recorded a 12th-place finish in Sunday's Nationwide Series event at Chicagoland Speedway.
"Unfortunately, Tony Jr. is no longer with the company," Earnhardt said. "I had hoped he would be here for a long time, but as we've discussed the direction of JR Motorsports moving forward, it was clear our differences in ideas were too vast to overcome."
Patrick has managed just two Top 10 finishes in 26 races in her first full-time year on the Nationwide circuit. Eury was tapped for the role of crew chief for JRM's No. 7 team when she debuted in 2010.
"I love Eury] like a brother, and you'll never hear me say a bad thing about him," Earnhardt added. "I know he'll have much success in anything he does going forward."
He said no decision had been made on who will take over this weekend at Kentucky Speedway.