The American will miss his second straight race as he struggles to overcome physical problems that began with a heavy crash at Sepang last year and were exacerbated in testing at the same track last month.
Pirro had also been slated to stand in for Spies at Jerez, only for Ducati to confirm he would, as originally intended, race its development bike at the Spanish track. The Italian finished 11th overall.
Pramac therefore entered just one bike, for Andrea Iannone, but the Italian crashed out of the race after suffering from arm pump.
He will undergo surgery on Tuesday, but is expected to be fit to compete at Le Mans on May 19.
A Pramac statement read: "Following today's additional medical check in Dallas, the doctor supervising Ben Spies recommended that the Texan undergo a period of extended rehabilitation.
"Despite his wish to return to the track as soon as possible, Spies will miss the French Grand Prix and will join the team again at the end of May, at Mugello."
- Sports & Recreation