The tremor was felt across Stockton, Billingham, Hartlepool, Wolviston and Middlesbrough just before 06:00 GMT.
People posted on social media to say they heard a rumbling or felt their houses shake. Emergency services said they received calls but there were no reports of damage.
The website Earthquake Track said it was six miles (10km) beneath Stockton.
The force said no-one was injured.
'Rather alarming'
The magnitude of the earthquake was first estimated as 2.8 by the United States Geological Survey but raised to 3.0 by the British Geological Survey following local analysis.
Seismologist Glen Ford described it as a "typical British earthquake" - strong enough to knock over ornaments, but of the kind you would expect to see three times a year.
"The UK is criss-crossed with many old tectonic plates, you get the stresses built up on them and these small earthquakes get released," he said.
"There are about 200 a year actually but only about 10% of them are felt by the general public so that's why when they happen they really startle people.
"This one occurred just under a heavily-populated area so many thousands of people felt it.
"In world terms it's absolutely tiny, but with its timing... people were just starting to come awake so it's rather alarming - gets them out of bed quite early."
Some people reported being woken up by it, and one person said: "The whole house shook and the electricity flickered."
One Stockton resident called Jason told BBC Tees: "There was a loud rumble, the door under the stairs popped open and then the house shook quite violently.
"It was quite an interesting way to wake up."
Other people reported feeling the tremor.
Some people posted on Twitter to say they heard loud bangs.
Comment: Despite the geologist claiming that this is fairly normal because the UK sees these kinds of quakes "three times a year", there have in fact been a significant number more - below are just some recorded in the last year: