Its the thirteenth tremor since fracking began last Monday and the biggest so far.
"Operations have now paused for the next 18 hours during which seismicity levels will continue to be measured", Cuadrilla said in a statement.
Under the "traffic light" system, the company must stop fracking for 18 hours after a tremor with a magnitude of more than 0.5, although those below 1.5 can not be felt at the surface.
Fracking is expected to resume at the site tomorrow morning.
But the exploration company said "micro seismic" events like this do not cause any damage and can not be felt at ground level.
The British Geological Survey recorded a 0.8 magnitude quake in the region of the site at about 11.30am on Friday.
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"Cuadrilla was hydraulicaly fracturing the shale rock adjacent to the horizontal well at the time and the seismicity is classed as a red event in line with the traffic light monitoring system regulated by the oil and gas authority".
Cuadrilla was forced to abandon fracking at the site in 2011 after two tremors measuring 2.3 and 1.5 on the Richter scale, respectively.
While fierce opposition from environmental activists prompted a court battle, a last-minute attempt to block the recommencement of fracking failed earlier this month.
Fracking resumed earlier this week after it was paused as a precaution following a 0.4 tremor on Tuesday.
Saturday's tremor is the 18th in the area since fracking recommenced 12 days ago. In that time there have been 17 earthquakes, including one today that has reached a red warning level, ' she said.
The only firm drilling for shale gas in Britain has temporarily suspended fracking after a mild natural disaster.
A spokesman for BGS said Friday's quake was recorded "right on top" of the Cauudrilla site and was the largest of 17 tremors there this month.
Fracking has already been suspended in Scotland, Wales and Northern Ireland due to perceived risks.