More than half of those registered as missing by the government are soldiers who were at the Speicher base which the jihadists captured six months ago near Tikrit.
"The number of missing from Speicher base has reached 1,660, from Badush prison 487, in addition to 554 from other areas, including 38 women," the ministry said in a statement.
Badush is a prison outside the northern city of Mosul, which IS has used as its main hub in Iraq.
The ministry said those numbers are based on applications filed by relatives and subsequent checking with the relevant ministries.
"The number of missing is likely higher than this," ministry spokesman Kamel al-Amin told AFP.
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He said some families who have been displaced by the violence or live in areas under jihadist control were not able to report a missing relative.
He added that the ministry had asked the families of those confirmed to be missing to provide DNA samples "in order to identify victims who might later be found in mass graves".
According to Human Rights Watch, IS gunmen executed up to 600 inmates from Badush prison on June 10, forcing them to kneel along a nearby ravine before pushing them in and setting fire to the bodies.
The following day, they seized the Speicher base and claimed to have executed 1,700 Shiite troops. The rights group was able to find evidence that at least 560 had been killed.
Major attacks on army bases in the western province in September are also believed to have left hundreds of troops dead or missing.
Rights organisations say the fate of hundreds of women and girls from the Yazidi minority who were abducted by IS during an August attack is still unknown.