Through his Twitter handle, Duale said the religion of Muslims superseded the curfew order.
“Muslims in Lamu County must go to the mosques for last 10 days Ramadan prayers despite the curfew,” one of his tweets said.
He however admitted enforcing security is paramount.
“Maintaining security in Lamu County is paramount but denying Muslim faithful their religious obligation on this holy month is unacceptable,” he added.
The Inspector General had said all people must remain indoors during the period the curfew is in force except under and in accordance with terms and conditions of a written permit granted by the County Commander.
“Due to insecurity in Lamu County, I David Mwole Kimaiyo, the Inspector General of Police of the National Police Service in accordance with the provision of the constitution section 8(1) of the public order Act Caps 56 laws of Kenya do hereby issue a curfew orders within Lamu County from 20th July 2014 to 20th August from 6.30pm to 6.30am.”
The month-long directive was due to take effect on Sunday evening.
Kimaiyo said the move was prompted by the spiralling insecurity in the county which has left over 90 people dead and property of unknown value destroyed.
The curfew was ordered to enable police effectively pursue armed militants who have staged a series of attacks in the restive county.