The current 5p charge will be doubled and will apply at all shops, not just large retailers, under the measures aimed at curbing plastic consumption.
An estimated 3.6 billion single-use bags are supplied annually by smaller retailers which are exempt from the current 5p bag levy.
Trade bodies representing around 40,000 small retailers have already launched a voluntarily approach to a 5p charge, but this accounts for less than one-fifth of England's estimated 253,000 small and medium-sized enterprises.
The changes, which could come into effect in January 2020, are contained in a consultation which has been launched by the Government.
In August, Theresa May promised there would be a consultation on changes to the levy by the end of the year despite reported opposition from the Treasury and Philip Hammond.
Mr Gove said: "The 5p single-use plastic carrier bag charge has been extremely successful in reducing the amount of plastic we use in our everyday lives.
"Between us, we have taken over 15 billion plastic bags out of circulation.
"But we want to do even more to protect our precious planet and today's announcement will accelerate further behaviour change and build on the success of the existing charge."
The 5p levy was introduced in England in 2015, with the money raised going to good causes rather than government coffers.
Association of Convenience Stores chief executive James Lowman said: "We welcome the Government's plans to extend carrier bag charging to all shops.
"This has been shown to be highly effective at reducing waste, whilst also raising money for local, national and environmental charities.
"Around half of small shops in England already charge for plastic bags voluntarily, with wider support for a mandatory charge."
Oceanographer Dr Laura Foster, head of Clean Seas at the Marine Conservation Society (MCS), said she hoped there would be support for the move.
The MCS has been monitoring the impact of the 5p charge since it was introduced in October 2015 and regularly provides evidence for government consultations.
Dr Foster told the Press Association: "We are able to measure the impact of legislation and we've seen that since the introduction of the plastic bag charge in the UK the amount we find on the beaches has gone down.
"That's also been replicated by studies that have been done offshore - they've also seen a reduction in the amount of plastic bags they find.
"So we do know that legislation can directly impact on the amount we find on our beaches and in our oceans."
Meanwhile, schools are being urged to end the consumption of single-use plastics by 2022.
Education Secretary Damian Hinds called on school leaders to stop using items such as plastic straws, bottles and food packaging in favour of sustainable alternatives.
"On my first school visit as Education Secretary almost a year ago, the very first question I was asked by a pupil was what we can do to limit the damage of plastic on the environment," he said.
"Reducing our use of plastic clearly is an important and timely issue which has captured the interest and the imagination of everyone in society."