The militiamen took items including clothing, shampoo and shaving cream from two shops in central Tikrit before driving away.
Two trucks were also seen leaving Tikrit loaded with new tyres, a generator and a mirror that fell out and shattered on the highway.
While localised, the incidents raise concerns over how the myriad militiamen now in the city will conduct themselves.
Baghdad turned to Shiite militias to bolster its flagging forces after Islamic State group (IS) jihadists led a sweeping offensive that overran large areas north and west of Baghdad last year.
They have played a major role in successful operations against IS, but have also been accused of abuses including summary executions, kidnappings.
Human Rights Watch said this month that both security forces and militias "engaged in deliberate destruction of civilian property" after breaking a months-long siege of the town of Amerli last year.
UN chief Ban Ki-moon said during a visit to Baghdad this week that Iraq must "bring volunteer armed groups fighting in support of the government under government control".
"Civilians freed from the brutality of Daesh should not have to then fear their liberators," he said, using an Arabic acronym for IS.