The minister's comments come after Prime Minister Sir Keir Starmer welcomed the end of the rule of al-Assad, who was overthrown and reported to have fled to Russia.
HTS and allied rebel factions seized control of the Syrian capital Damascus on Sunday after years of civil war.
Under the Terrorism Act 2000, the home secretary may proscribe an organisation if they believe it commits or participates in, prepares for, promotes or encourages, or is otherwise concerned in terrorism, and if it is proportionate to do so.
It is a criminal offence to join a group on the list. It is also against the law to arrange a meeting if it is to support the activities of a proscribed organisation.
HTS's leader Abu Mohammed al-Jolani, who has now started using his real name, Ahmed al-Sharaa, cut ties with al-Qaeda in 2016. He has recently pledged tolerance for different religious groups and communities.