It came two days after a magnitude 1.55 tremor which was the largest ever tremor at the site run by Cuadrilla in Preston New Road, Lancashire.
Friday's tremor was detected at 11.22pm.
The company said it lasted for less than one second and "the measured vibration at ground level during the event was approximately 0.4 mm/s".
"This micro seismicity followed today's pumping operations," it said.
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"The integrity of the well has been confirmed."
A smaller 0.53 magnitude tremor occurred just after 5am on Saturday and also lasted for less than one second, the company added.
Fracking was temporarily stopped at the Cuadrilla site after Wednesday's tremor.
Pausing work for 18 hours is the routine response for any tremor over 0.5.
A Cuadrilla spokesman said on Thursday that most people who live near the Preston New Road facility would not have noticed Wednesday's movement, which would have felt similar to someone dropping a large bag of shopping on the floor.
"Minor movements of this level are to be expected and are way below anything that can cause harm or damage to anyone or their property," he said.
Labour's shadow business secretary Rebecca Long Bailey has called for fracking to be banned, saying it causes air and water pollution and contributes to climate change.
Environmental campaign group Friends of the Earth said in 60 days of fracking last year there were 57 tremors in Lancashire and that it cannot be carried out without triggering earthquakes.
"Even small vibrations at ground level can be the sign of far more damaging impacts deep underground," said Jamie Peters, a campaigner for the organisation.
The Government has said the extraction of shale gas through fracking could support the UK's transition to net zero greenhouse gas emissions.
– Padraig Collins, Press Association