Thieves took a large amount of lead from the roof of the minster without consideration for the interior of the centuries-old building.
Without the waterproof lead covering, everything inside the building has been at risk of damage from rainfall.
The Rev Kevin Partington, minster rector, said a number of sections of the church, including the disabled toilets, nappy changing facilities and the popular heritage centre were covered in dust, dirt and rain which fell through the unprotected roof.
The minster is in the midst of a fundraising drive to pay for vital refurbishments to the building and repairs to the organ.
He said: "It has caused complete and utter disruption with the rebuilding work. It has put everything at risk.
"We are determined that the people who did this won't get the last word – we will carry on and continue the work.
"The main area where the water ran in was over the heritage centre. Lots of people visit to come and see the history of Dewsbury, and we are immensely proud of the minster's role in the life of the town."
Mr Partington said the roof needed to be repaired as soon as possible – but he had no idea how much it would cost.
He added: "It feels like a kick in the teeth. It's vandalism on a huge scale."
Dewsbury police said investigations into the incident were on-going, and urged anyone with information to contact them on 01924 431072.
You can email Lauren Chadwick at lauren.chadwick@ywng.co.uk