A message sent to all military bases across the region called for “all units and troops to remain at alert and not be taken by surprise”.
Two armoured cars and two all-terrain pickup trucks were taken after the jihadists tried to take over a military base at the village of Mainok in Borno state on Wednesday.
Troops repelled the assault with reinforcements from the nearby town of Benisheik. The attack was the latest against “hard” military targets in recent weeks.
At least nine Boko Haram fighters were killed in the hour-long shootout, which forced motorists on the Maiduguri-to-Damaturu road to take cover until it had ended.
The army message, which was seen by AFP, also said: “All troops to ensure they check all vehicles and not to assume as BHT (Boko Haram terrorists) may disguise as own forces.
“Initial assessment at the moment suggests that 2 VBL (armoured vehicles) and 2 Hilux (pick-up trucks) are missing and for the moment we assume carted away.”
AFP contacted the army about the message but there was no immediate response.
In September 2013, Boko Haram disguised as soldiers barricaded the Maiduguri-Damaturu highway at Benisheik, some 10 kilometres (6 miles) from Mainok, and killed 167 people.
Militants from the Islamic State group affiliate have routinely used stolen military vehicles and weapons to conduct attacks.
Nigeria maintains that the counter-insurgency begun in early 2015 has left Boko Haram a spent force, after eight years of violence that has killed at least 20,000 people.
But attacks, including suicide bombings against civilians, have continued, casting doubts on that claim.
Later on Thursday, Nigerian state governors approved a plan to provide an extra $1 billion (850 million euros) to fund the fight against Boko Haram.
The state governor of Edo state in southern Nigeria, Godwin Obaseki, told reporters in Abuja the money would be taken from the federal government’s excess crude account.
The account was set up to save money made on oil sales above a benchmark outlined in the country’s budget.