Unconfirmed reports from the African country on Sunday suggested Mwepu had suffered a suspected heart attack.
Mwepu was forced to retire from football earlier this season because of a hereditary heart condition and was appointed an academy coach at Brighton at the start of January.
"The club can provide the following update on Enock Mwepu, in response to media reports," a statement from Brighton read.
"Enock was taken unwell in Zambia and is currently undergoing precautionary checks. Our medical team is in communication with the hospital to assist if required.
"The club would like to thank the many well-wishers for their messages and support. The club nor Enock wish to provide any further comment at this stage."
Mwepu was adviced by medical experts to quit football back in October after a heart issue was discovered while on international duty with Zambia.
At just 24 years of age, Mwepu's condition was described as hereditary and his risk of developing a cardiac arrest was high if he continued playing.
Mwepu played in all six of Brighton's opening Premier League games this season.
He joined Brighton from Red Bull Salzburg last summer and made 18 appearances in the Premier League, scoring two goals and providing four assists.
Mwepu made 23 appearances for the Zambia national team and scored six goals.
