Sajid Javid today said that offering young people the vaccine by this date will allow those teenagers in that age bracket to have the two weeks necessary to build maximum immunity before returning to school in September.
People aged 16 and 17 will be able to get vaccinated at one of more than 800 GP-led vaccination sites, the Department of Health and Social Care (DHSC) said.
Thousands will be invited, including by text and letter, to book their appointments through GPs or via walk-in centres, it added.
Mr Javid said: "It is brilliant to see tens of thousands of young people have already received their vaccine - thank you for helping to further build our wall of defence against Covid-19 across the country.
"I have asked the NHS in England to ensure they offer a first dose of the vaccine to everyone aged 16 and 17 by next Monday, August 23, this will make sure everybody has the opportunity to get vital protection before returning to college or sixth form.
"Please don't delay - get your jabs as soon as you can so we can continue to safely live with this virus and enjoy our freedoms by giving yourself, your family and your community the protection they need."
Some 100,000 text messages are also being sent to teenagers within three months of turning 18, inviting them to book their vaccine appointment online through the National Booking Service or by calling 119.
Children aged 12 to 15 who are clinically vulnerable to Covid-19 or who live with adults who are at increased risk of serious illness from the virus are also being contacted by the NHS and invited for their vaccine by August 23, the DHSC said.
The latest data, published on Thursday, showed that 70 per cent of people aged 18 to 29 in England had received a first dose of vaccine up to August 11, suggesting 30 per cent are unjabbed.
By contrast, take-up for first doses among 30-39 year-olds in England now stands at 81.2 per cent, while for 40-49 year-olds it is 89.1 per cent, according to NHS England estimates.
All other age groups are more than 90 per cent.
The Government has repeatedly urged young adults to come for a first jab, with special "grab-a-jab" pop-up vaccine centres opened across the country and a number of food delivery and taxi-hailing companies enlisted to offer discounted rides and meals for customers who have received a first dose.
Uber, Bolt and Deliveroo are among the brands that have agreed to offer incentives to encourage younger people to get vaccinated.
The vaccine rollout in England is now estimated to have prevented between 22.9 and 23.8 million infections and between 81,300 and 87,800 deaths, according to the latest research from Public Health England (PHE).
Dr Nikki Kanani, NHS deputy lead for vaccination programme in England, said: "Thanks to the dedication and hard work of NHS staff, well over 39 million people in England have already had their first, including more than a quarter of a million young people under the age of 18.
"Now, as teenagers prepare to head back to school or college or into their first full-time jobs, once again NHS staff are doing everything they can to offer young people the lifesaving vaccine as quickly as possible to protect themselves and others.
"Those who are eligible should check their nearest walk-in centre on the site-finder today or book through their GP team once invited to do so."