One of the organisation's storage rooms at St Catherine's Business Complex in Broad Lane, Bramley, was ransacked on Friday night.
The door had been forced open and items donated to the baby bank were strewn across the unit.
And as volunteers took stock yesterday, it became clear that items including a new boxed high chair, bags of new toys, nappies and soaps had been taken.
Leeds Baby Bank partner and trustee Faye Freeman said: "We've got people coming to collect those items that are gone. They were bundled up ready to go out to vulnerable people tomorrow.
"We will be able to reorganise but we are teams of volunteers and we do it in our spare time. These poor people are going to have to wait a few days now."
Items taken included toys donated through Radio Aire's Cash for Kids scheme, while clothing given through Mothercare's Gift-a-bundle had been torn from their bags.
Burglars struck as volunteers celebrated first anniversary
The exact timing of the break-in is not yet known, but it may have happened while the team held its annual general meeting and a party to celebrate the baby bank's first anniversary at Shine in Harehills.
It only came to light when another tenant found new boxed prams and other items just inside the entrance to the complex the next morning.
Upon further investigation, he found a delivery business had been broken into and the burglars had smashed through an adjoining door to get into one of the baby bank's four rooms.
The room in question is used to put together care packages ready for collection by families who have been referred to the volunteer-run organisation.
The burglars had also tried to break into a room used to store donated prams, but failed to do so.
It is believed they may have been disturbed, leaving some items at the complex entrance in their rush to get away.
Police are now investigating and forensic work has been carried out at the scene.
"We won't be beaten"
In the meantime, the baby bank team are determined to get things back on track as quickly as possible.
"The support we get from the public is amazing," Faye said.
"We had a joiner message us to say he'd come and fix our damaged door. There's lots of people offering to buy us replacements for things missing.
"I love the people of Leeds - they are amazing."
Since it was founded by a group of Leeds mums in January 2016, the volunteer-run organisation has supported around 600 different families.
It is also looking for new premises in the city so that more parents in need can be helped in the year ahead.
Faye said: "There are exciting things to come and we won't let it get us down.
"The main thing is nobody was hurt. Things will get replaced, we won't be beaten."
Anyone wishing to help the baby bank can make a donation via its GoFundMe page.