A man charged with attempted murder after he allegedly fired an arrow at a teenage girl in a supermarket near Brisbane will remain behind bars.

Benjamin Jeremy Bourke, 25, allegedly shot the 15-year-old in the hand and stomach after walking into Booval Aldi in Ipswich on Tuesday afternoon.

Police say Mr Bourke was wearing a black hoodie and a mask when he was spotted walking from Booval Railway Station along South Station Road holding a compound bow about 4.40pm.

He allegedly shot an arrow at a woman who was jogging but missed.

The Bundamba man then allegedly fired an arrow at a passing car before going into the supermarket, where he shot a third arrow, hitting the teenager.

Passers-by restrained Mr Bourke until police arrived.

The girl suffered injuries to her stomach and hand that were not considered life-threatening. She was taken to Queensland Children’s Hospital, where she remains in a stable condition.

The pair did not know each other.

Mr Bourke was not required to appear in Ipswich Magistrates Court on Wednesday, where he also faced charges of torture and going armed so as to cause fear. He was remanded in custody to appear in the same court on October 4.

Outside court, defence lawyer Dylan Hans said he was unsure if his client would contest the charges.

Police are continuing their investigations at Booval Aldi, which remained closed to the public on Wednesday afternoon.

-with AAP