Officials had said firings could start this month for staffers who missed vaccination deadlines last fall.
Plans to deploy the software in Ohio in March are being pushed back almost two months.
A total of 1,200 Guard members will be deployed to more than 50 hospitals across the state, KATU-TV reported.
Roughly half of the military's 88 COVID-19 deaths have been among Army reservists.
Federal officials are expected to distribute 500 million coronavirus test kits in coming weeks.
The report was due out on Jan. 31 but will be delayed by six weeks.
The military reported 72 deaths overall in 2021.
Defense Secretary Lloyd Austin announced he tested positive for COVID-19 on Sunday.
The department recorded more than 27,000 cases on Thursday morning, almost 30 percent above its January high.
The move is part of a broader response to the surge in cases of the Omicron varinant in recent weeks.
