The 60 year-old man, who does not wish to be named, was taken to Pinderfields Hospital in Wakefield after the incident at Normanton Brick Company Ltd in Altofts in December 2010.
Surgeons managed to reattach the hand where it had been partially separated using nerve and tissue from his legs.
Leeds Crown Court heard that the worker had started to run a double press brick-making machine, which extends across two rooms and two storeys, at the start of the shift.
He was then told the bricks being produced were below standard as the press plates were clogged up with clay and dirt.
The worker stopped the machine so he could clean under the plates but, as he used his gloved hand to remove the dirt, the machine re-started.
His hand was drawn into the machine and the re-press came down, severing his thumb and slicing though his hand, leaving it only partially attached.
Normanton Brick Company Ltd of Altofts was fined £15,000 and ordered to pay £6,307 in costs for safety breaches.
After sentencing, HSE Inspector Jackie Ferguson said: “Normanton Brick Company had not carried out a suitable and sufficient risk assessment.
“Had they done so they would have identified failings in the standard of guarding on the brick press.”