The source said the hangings took place in Nasiriyah prison, where death row prisoners are held.
Those not executed for "terrorism" were sentenced over "criminal cases".
Rights group Amnesty International says it recorded more than 45 executions in Iraq last year, including many of people accused of belonging to the Islamic State group.
A 2005 law carries the death penalty for anyone convicted of "terrorism," which can include membership of an extremist group even if they are not convicted of any specific acts.
Rights groups have warned that executions were being used for political reasons.
Since Baghdad officially declared victory over IS in 2017, Iraqi courts have sentenced hundreds to death for crimes perpetrated by the jihadists who had set up a "caliphate" in territory seized in Iraq and Syria in 2014.
Only a small proportion of the sentences have been carried out, as they must be approved by the president.
Barham Saleh, who has held the post since 2018, is known to be personally against capital punishment.
According to an AFP tally, at least 14 people sentenced for "terrorism" have been executed in Iraq since the start of the year, all at the Nasiriyah prison.
Earlier this month, a man who murdered a senior Iraqi official in broad daylight was sentenced to death amid revulsion over the government's failure to halt a wave of assassinations.
In January, an official from Iraq's presidency told AFP more than 340 execution orders "for terrorism or criminal acts" were ready to be carried out.
Another presidency official said that all the orders were signed after 2014, most of them under ex-president Fuad Massum and at a time when IS occupied a third of the country.
Rights groups accuse Iraq's justice system of corruption, carrying out rushed trials on circumstantial evidence and failing to allow the accused a proper defence.
UN human rights experts in November urged Baghdad to halt all "mass executions".
