The Cancer Support Scotland Centre is being built in the grounds of Gartnavel Hospital, in the West End.
But when builders arrived at the site, they found drills, sanders, a jigsaw cutter and a router had been taken.
The thieves even unscrewed the wooden shutters on the centre and then put them back on – so it would look as if the building had not been disturbed.
Police believe the thieves targeted the Great Western Road site between last Thursday evening and Friday morning.
Colin Graham, the charity's chief executive, said: "What these people have done is heartless and has angered us all.
"We plan to move into our new centre in under three months, but there is still a lot of work to do and the construction workers got little done on Friday."
Police have been reviewing local CCTV footage and have appealed for information on the robbery.
A spokeswoman said: "We are investigating a report of a break-in and theft of tools worth a four-figure sum. Inquiries are continuing."
The facility is due to open in August and will be named the Calman Centre, in honour of Professor Sir Kenneth Calman, who founded the charity.
It will triple the charity's services, creating 8000 appointments for patients each year.
The building will also expand existing services to include a befriending service; a hair, nail and foot salon; a library; a cafe and courtyard garden.
The charity has raised £255,000 to allow Glasgow Building Preservation Trust to renovate the B-listed former Gartnavel Hospital church.
However, it still needs to raise another £165,000 to cover operating costs for the first year.
On Monday, we told how Evening Times readers had rallied behind the campaign to raise almost £500,000 for the cancer support centre.
Sir Kenneth Calman founded the charity – originally named Tak Tent, meaning take care – in 1980.
Cancer Support Scotland provides free complementary therapies, counselling and advice to patients coping with a diagnosis or undergoing chemotherapy.
As well as self-referrals, the charity takes patients from other major charities, including Macmillan Cancer Support and Maggie's.
Anyone with information on the theft is asked to call Partick police on 0141 532 3500.
The charity needs to raise the remaining funds to buy the building and kit it out. To donate to the centre, call 0141 211 0122 or see: www.cancersupportscotland.org