The blaze was reported in the early hours of Saturday morning.
"It is with a heavy heart we have to let our customers know that we will be closing temporarily," a post on the cafe's Facebook page said.
"In the early hours of Saturday morning, we were alerted of a fire at our beautiful establishment.
"The fire has caused severe damage to the building, meaning we will be unable to open for some time.
"We would also like to thank the Lincoln community for the all love and offers of help and support we have received.
"This is not the end, we will be back serving you our delicious meals and cocktails as soon as we can."