The MRC leader was arrested on Monday.
Omar Mwamnuadzi was detained during a gunfight at his home, in which two people were killed.
A local Kenyan official was then hacked to death in a retaliatory attack, police say.
Tension has been rising in Kenya ahead of general elections due in March 2013.
There were riots in Mombasa, the main city in Coast province in August, after a Muslim cleric accused of supporting the Somali group al-Shabab was shot dead.
In July, Kenya's High Court lifted a ban on the MRC, which the government had outlawed in 2010 after accusing it of being a criminal gang.
However, regional police chief Aggrey Adoli on Monday told the BBC's Focus on Africa programme that despite the court ruling, the group was "still illegal".
The MRC accuses successive governments of marginalising the ethnic groups living along the coast, which is the centre of the country's tourism sector, and giving land to outsiders.
Calls for the secession of the mainly Muslim coastal region tend to intensify in the run-up to general elections, analysts say.[/ht,l]