The church is in the care of charitable organisation The Churches Conservation Trust, who say they were left devastated when the damage was discovered.
A statement on their Facebook page described the damage.
It said: “The faces of saints and of Jesus Christ have been used for what can only be described as target practice. “Carefully aimed projectiles have fractured specific areas of the glass, mainly several heads and faces of the depicted human figures and animals.
“Examination of the centres of impact, which are circular and measure about 3mm to 5mm in diameter, would suggest an airgun pellet or small stone fired by a catapult.
“Some of the damage is at a height too great to have been attacked from ground level except with some kind of long implement using exceptional force.”
Built in 1859 to replace a medieval church, this is the third place of worship on this site, the earliest dating to the 1100s.
Its precious stained glass, painstakingly created by artists and craftsmen - made by Lavers, Barraud and Westlake - was installed between 1860 and 1890.
The south windows depict Christ and the Doctors and the Presentation in the Temple.
The impressive west window, donated by Lysimachus Parker, who died in 1860, shows Noah’s Ark, the Baptism of Christ and the Crossing of the Red Sea.
The statement continued: “This heritage crime attack is particularly upsetting to local people from the tiniest parish in East Lindsey who cherish this church and who saved it from certain demolition in 1996 after it was declared structurally unsound.
“We at The Churches Conservation Trust became involved in that year and we now own this historically significant building, keeping it open for everyone to visit and use.
“Our conservation team are inspecting the damage and specialist stained glass experts will be brought in to evaluate the best way to repair the damage.
“Sadly this will likely cost thousands of pounds.
“Please consider helping us to repair the damage caused to this beautiful church.”
• To donate £5, please text LCA to 70970 or to donate £10, please text LCA to 70191.
Alternatively, donate online at visitchurches.org.uk