He was taken into custody from Ransi village in East Pagla Union of South Sunamganj Upazila on Tuesday, said Lt Commander Faisal Ahmed of RAB-9.
Mohsin, 25, hails from Tukerbazar Shahpur Talukdarpara in Sylhet Sadar Upazila.
He went into hiding after law enforcers launched an operation to nab him, said Faisal.
Mohsin had threatened to kill Shakib for visiting a Kali Puja programme in Kolkata. He came on Facebook Live in the early hours of Monday and verbally abused Shakib, threatening to hack him to pieces with a sharp object.
Later, on Monday morning, Mohsin came on Live again and apologised for his previous video and called on Shakib to apologise to the nation.
Afterwards, law-enforcement agencies launched a manhunt to arrest Mohsin. Members of RAB and police went to his house in the early hours of Tuesday in Talukdarpara and interrogated his family members.
Police have also filed a case against Mohsin under the Digital Security Act with Jalalabad Police Station.