Kent Police said the victim, in his 40s, was found with injuries consistent with stab wounds in Sally Port Gardens, Gillingham, on Tuesday at around 5.55pm.
Police have arrested a 24-year-old man on suspicion of attempted murder.
Nearby to the incident is Brompton Barracks, the historic home of the Royal Engineers. Sally Port Gardens road is the location for Lampard Centre, which is used for activities by soldiers and their families.
The Ministry of Defence has been approached for comment but a source said it was “too early” to identify the victim as a soldier.
A Kent Police spokesman said: “Police were called to a report of a serious assault in Sally Port Gardens, Gillingham.
“A man in his 40s suffered injuries consistent with stab wounds and was taken to hospital for treatment. His condition is currently described as serious.
“Officers attended and at around 6.20pm they arrested a 24-year-old man on suspicion of attempted murder.
“A cordon is currently in place around the scene of the incident and enquiries to establish the circumstances are ongoing.
“Residents are advised to expect an ongoing police presence in the area.”