Askew was involved in an ugly crash during last month's Indy 500 when his car slammed into the wall at the entry to the pit lane, destroying his car.
The IndyCar rookie was cleared to race at events in St. Louis and Mid-Ohio but later reported balance and coordination issues.
After being examined by the Indycar medical team Askew was ruled unfit to race at Harvest GP in Indianapolis on Oct. 2-3.
"This was an incredibly tough call but I have to follow the advice of the IndyCar medical team and my doctors," Askew said in a statement. "My priority right now is focusing on my health."
Askew has had three top-10 finishes in his rookie campaign, including a third place in Iowa.
Castroneves is one of the most successful IndyCar drivers of all-time with 30 career wins all with Penske racing but the 45-year-old Brazilian has not raced full-time in the series since 2017. (Reporting by Steve Keating in Toronto, Editing by Ed Osmond)