Sajid Javid tweeted that he had updated G7 health ministers on what is known about the spread of the virus. There are now 20 cases recorded in the UK.
Globally, 127 cases have been reported in 11 countries, according to John Brownstein, professor of medicine at the Harvard Medical School in the US, who is keeping track of global cases.
Mr Javid said: "Most cases are mild, and I can confirm we have procured further doses of vaccines that are effective against monkeypox."
The Government has some stocks of the smallpox vaccine, which can be effective against monkeypox as the viruses are quite similar.
This is being offered to very close contacts of those who have been affected.
Monkeypox cases are usually found in West Africa, and the virus does not often spread elsewhere.
That is why outbreaks reported across Europe, Canada, Australia and the United States have caused alarm among public health experts.
The disease, which was first discovered in monkeys, is usually mild but can cause severe illness in some cases.
Symptoms of monkeypox include fever, headache, muscle aches, backache, swollen lymph nodes, chills and exhaustion.
A rash can develop, often beginning on the face, which then spreads to other parts of the body including the genitals.
The rash can look like chickenpox or syphilis, and scabs can form which then fall off.
The incubation period of monkeypox is usually from six to 13 days but can range from five to 21 days.
The cases in the UK are not all one cluster, with separate cases springing up that are unconnected.
The first case identified was in a person who had returned from Nigeria but other cases are unrelated to travel, suggesting there is community transmission.
Several cases have been confirmed in gay, bisexual and other men who have sex with men who have attended sexual health services.
Monkeypox is not normally a sexually-transmitted infection, but it can be passed on by direct contact during sex.
It can also be spread through touching clothing, bedding or towels used by someone with the monkeypox rash, and through the coughs and sneezes of somebody with the infection.
The UK Health Security Agency (UKHSA) said monkeypox does not usually spread easily between people and that the risk to the UK population remains low.
Anyone with unusual rashes or lesions on any part of their body, especially their genitalia, should contact NHS 111 or call a sexual health service if they have concerns, it said.
Dr Susan Hopkins, chief medical adviser at the UKHSA, said: "We anticipated that further cases would be detected through our active case finding with NHS services and heightened vigilance among healthcare professionals.
"We expect this increase to continue in the coming days and for more cases to be identified in the wider community. Alongside this we are receiving reports of further cases being identified in other countries globally.
"We continue to rapidly investigate the source of these infections and raise awareness among healthcare professionals.
"We are contacting any identified close contacts of the cases to provide health information and advice.
"Because the virus spreads through close contact, we are urging everyone to be aware of any unusual rashes or lesions and to contact NHS 111 or a sexual health service if they have any concerns.
"Please contact clinics ahead of your visit and avoid close contact with others until you have been seen by a clinician.
"A notable proportion of recent cases in the UK and Europe have been found in gay and bisexual men so we are particularly encouraging them to be alert to the symptoms and seek help if concerned."
The World Health Organisation said monkeypox had been a "priority pathogen" for years and its Strategic and Technical Advisory Group on Infectious Hazards with Pandemic and Endemic Potential (STAG IH) was meeting on Friday.
Jimmy Whitworth, Professor of International Public Health at the London School of Hygiene and Tropical Medicine (LSHTM), said the outbreak in the UK was "unprecedented".
He said: "There is a need to engage with the at-risk community of gay and bisexual men to ensure they know about the presence of this infection and report any sign and symptoms to health facilities.
"Cases need to be identified, isolated and treated, either in hospital or at home, depending on severity and circumstances.
"Close contacts need to be identified and monitored for signs of infection. Monkeypox is not very transmissible and with these measures the outbreak can be quickly brought under control."