Army spokesperson Colonel Sani Usman said the trio tried to attack internally displaced people (IDPs) collecting water at a well on the outskirts of Monguno, in Borno state, at about 06:15 (05:15 GMT).
Two of the three women, who he described as "Boko Haram terrorists suicide bombers" were shot and killed, causing their explosives to detonate, injuring two civilians.
The third suspect's explosives went off about an hour later at a nearby location, Usman said.
The attempted attack came just before the end of the Muslim holy month of Ramadan, which is marked in Nigeria with two days' public holiday – Tuesday and Wednesday.
It also follows a similar attempted suicide bombing at a mosque in the Borno state capital, Maiduguri, on June 27, which saw two men try to target Ramadan night prayers at a city mosque.
Both incidents underlined the threat posed by Boko Haram, which has used suicide bombers against civilian "soft targets" as part of its seven-year insurgency to create a hard-line Islamic state.
A military counter-offensive waged since January last year has pushed out the militants into remote border areas around Lake Chad. The rate of attacks has declined in recent months.
Borno governor Kashim Shettima meanwhile announced there would be no restriction on movement in or out of the state during the celebrations to mark the end of a month of fasting and prayer.
It is the first time in six years that restrictions will be lifted.
But Shettima said "stringent security measures" will be in place at prayer grounds, where large crowds were expected.