The threat came after media outlets reported an influx of Somali women and their children seeking medical help in Lamu county.
This was especially in areas close to the border, including Basuba, Kiunga and Ishakani in Lamu East.
Early this week, the militants threatened people living in areas under their control with dire consequences, if they seek treatment from kuffars or non-Muslims who are offering the help.
But the parents and their children have defied the warning by the terror group linked to al Qaeda.
Lamu Health services director Dr David Mulewa said this week that the influx could lead to the outbreak of infectious diseases.
Mulewa said the migrants do not have immunisation records or the status of the Somalia children entering the county.
But he added that the county launched monthly immunisation programmes for various diseases, for children along the border areas of Kiunga and Ishakani.
The terror group has been carrying out sporadic attacks in several parts of the country in response to Kenya’s presence in Somalia, as part of the Amisom peace keeping force.
An attack on Arabia police post in Mandera county saw them steal BVR kits, a police vehicle and weapons. They also destroyed communications masts, breaking the link between officers and their commanders. The officers withdrew after they were overpowered.
Al Shabaab has also attacked KDF camps in Somalia, leaving many dead.
The al Qaeda-linked terror group said its fighters killed at least 66 people when they overran the camp in Kulbiyow near the Kenyan border on January 27.
In January 2016, al Shabaab said it had killed more than 100 Kenyan soldiers in El Adde, a Somali camp near the border with Kenya. The Kenyan military never gave details of casualties, but Kenya media reports suggested a toll of that magnitude.