Stricker, 46, who by design has played a limited schedule this year, has a hamstring injury suffered while water skiing recently. He played through the injury at the WGC-Bridgestone Invitational and the PGA Championship.
Stricker is ranked 13th in the world and 19th in the FedEx Cup standings.
The 37-year-old Johnson, competing this week at the Wyndham Championship in Greensboro, N.C., will skip the Barclays because he's the best man at his brother Gabe's wedding next weekend. Coming off four consecutive top-10 finishes, he is ranked 25th in the world and 23rd in the FedEx standings.
Both players are expected to compete the following week at the Deutsche Bank Championship, the second playoff event, outside Boston.
After the Wyndham, the top 125 players in FedEx Cup points will advance to The Barclays, to be played Aug. 22-25, at Liberty National in Jersey City, N.J. From there, the top 100 players will advance to the Deutsche Bank. The top 70 after that event will move on to the BMW Championship outside Chicago, and the top 30 from there will head to the Tour Championship. The winner of the FedEx Cup will receive a $10 million bonus.