Mr Lamin was one of the RUF members who gained cabinet seats in exchange for a rebel ceasefire, as part of the peace accord signed by the government and the RUF in Lome last year.
Mr Sankoh's Revolutionary United Front (RUF) has been accused of taking hostage several hundred United Nations peacekeeping troops who are in Sierra Leone to oversee the rebels' disarmament.
The United Kingdom has meanwhile announced the evacuation of UK citizens from Sierra Leone.
The missing UN peacekeepers are part of a force sent to Sierra Leone to enforce a peace deal signed last year by President Kabbah and the RUF - a deal which has recently appeared close to collapse amid repeated violations by the rebels.
Shooting broke out outside Mr Sankoh's Freetown home, which is guarded both by UN soldiers and RUF fighters, after thousands of people gathered to denounce the RUF.
Our correspondent Barnaby Phillips says there was a "charged" mood in the crowd, with some people calling for Mr Sankoh and his supporters to be forcibly disarmed.
The RUF guards fired into the crowd using automatic weapons and rocket-propelled grenades.
'Coup plot'
Trade Minister Mike Lamin was among several RUF officials detained for questioning by the military police in connection with an alleged plot to overthrow President Kabbah.
Mr Lamin was one of the RUF members who gained cabinet seats in exchange for a rebel ceasefire, as part of the peace accord signed by the government and the RUF in Lome last year.
Reports say Mr Lamin was arrested on Sunday, later released and then re-arrested. It is not known whether he has again been released.
The arrest was ordered by Johnny-Paul Koroma - the army commander who himself staged a coup against President Kabbah in 1997 - but who has now declared his loyalty to the president following the restoration of civilian rule.
Mr Koroma said the arrests had been authorised by President Kabbah "to put things on course again" - a reference to the Lome peace agreement.
Militia
On Sunday, both the president and Mr Koroma hinted that it might be necessary for Sierra Leonean loyalists to offer armed resistance against a rebel attack.
Addressing the nation on Sunday, Mr Sankoh sought to assure citizens that the government had "an effective contingency plan in place which will be activated in the unlikely event that Unamsil is unable to provide adequate security in the face of aggressive action".
He gave no further details.
Mr Koroma told the BBC that "we just have to find ways and means to defend the people and ourselves", involving various civilian militia groups.
Asked whether this would involve the army handing out weapons, Mr Koroma replied: "We are not offering guns at the moment. We are saying that we cannot sit by and see this country be torn apart."
Britons to leave
UK Foreign Secretary Robin Cook told parliament that an evacuation plan had been activated and the British High Commission in Freetown would be contacting British nationals.
An advance force of about 250 British paratroopers arrived just outside the city earlier on Monday and began to secure the international airport.
More troops have been flown to nearby Senegal and warships including the aircraft carrier HMS Illustrious will reach the area within days.
On Saturday night British military advisers flew into Sierra Leone to advise the UN on its operation there.
The team of about a dozen men will be based in Freetown, where they will assess the technical support needed to enhance the effectiveness of the UN's 8,000-strong force.