It is thought Daisy, who was named by the firefighters, had wandered from her field in the area of Brow Lane overnight and fell into the hole.
She was spotted by an early morning dog walker who alerted the farmer, who tried to free Daisy himself.
He called the Fire Service at around 6.45am who sent the Technical Rescue Unit and a fire engine from Cleckheaton Fire Station.
Nine firefighters attended the scene to free Daisy, who trapped under a large rock weighing around 3,000 kilos. Once this was removed, the calf was harnessed and lifted free.
Technical Rescue Officer Chris Lawton said: “This is kind of rescue is not 'un-herd' of but it was particularly challenging because of the tight spot Daisy got herself into.
“We think she may have been there all night as she was quite tired and mum was making a lot of noise in the nearby field.
“As firefighters we don't like to milk our successes but we were particularly chuffed with this one.”
Daisy was unharmed apart from bumps and bruises and was freed and returned to the field at 8.45am.