The engines can stall or a rear suspension part can fall off, according to multiple media reports.
U.S.-listed shares of Subaru fell 0.72% to $9.64 in trading Tuesday.
The recall starts on May 28.
The engine recall covers more than 466,000 Crosstrek SUV models from 2018 and 2019, and Impreza car models manufactured from 2017 through 2019, the company said.
The company said that a computer can power the ignition coil after the car is shut off, according to government documents cited in media reports. That can cause a short circuit.
Dealers will update the software, replace ignition coils and if necessary install a new front exhaust pipe.
The suspension recall covers more than 408,000 models of Crosstreks from 2018 and 2019, and Foresters models from 2019.
Some rear stabilizer bar bolts can loosen and detach, increasing the risk of a crash.
Dealers will tighten bolts and replace any missing ones, beginning May 14.
Separately, Subaru said on Tuesday that it was suspending production at its plant in Indiana through the end of April due to a global shortage of semiconductors.
A Subaru spokeswoman said 15,000 vehicles for North America would be affected, according to a report in Reuters.