According to reports, an argument between the pair is said to have started over a girl.
Swannell is suspected of cutting his jugular vein with a broken beer bottle after an initial punch-up.
Local newspapers said Mr Vigors, who was not part of the cricket tour, died within minutes of a friend removing a large piece of glass lodged in his throat as he collapsed on the floor in the early hours of Saturday morning.
A spokesman for the Civil Guard in Majorca, which made the arrest, said: "We are questioning a British man after a compatriot was killed in a bar in Magalluf following an argument. The victim suffered various cuts to his throat which resulted in damage to his jugular vein.
"He bled to death at the scene before paramedics arrived. We are quizzing the man currently in custody as a murder suspect."
A Foreign Office spokeswoman said: "We can confirm the death of a British national in Magaluf in Spain. Consular staff are in contact with the next of kin and providing consular assistance."