Cervelli suffered the injury in Sunday night's game against the Boston Red Sox and was diagnosed with a Grade 2 hamstring strain the following day.
Murphy, 22, batted .154 in 16 games with New York last season and will serve as a backup to Yankees catcher Brian McCann, who avoided a potentially major injury after a ball ricocheted off his right hand Sunday night.
The Yankees optioned reliever Shane Greene to Scranton on Monday to create a roster spot for Sizemore, who should provide depth to New York's injury-plagued infield.
The Yankees already are without first baseman Mark Teixeira, who is on the DL with a hamstring injury, and played Sunday's game without shortstop Derek Jeter (quad) and second baseman Brian Roberts (back).
A source told ESPNNewYork.com on Monday that despite the rash of injuries, the Yankees will not sign free-agent shortstop Stephen Drew or first baseman Kendrys Morales. New York's infield void could be filled by the versatile Sizemore, who has played both second base and third base in three seasons with the Detroit Tigers and Oakland Athletics.
A former top prospect in Detroit's organization, the 29-year-old Sizemore was batting .344 in 10 games at Scranton.
ESPNNewYork.com's Wallace Matthews contributed to this report.