Francis Thackeray, from the University of the Witwatersrand in Johannesburg, said that he was "very interested in the possibility" of examining Shakespeare's grave.
"Given the extraordinary success of the study of the skeleton of Richard III, we recognise the potential of undertaking forensic analyses of the Bard," he said.
Shakespeare, who died in 1616, is buried in the chancel of Holy Trinity Church in Stratford-upon-Avon.
Thackeray believes that his bones could tell us much about how he lived: what he ate and drank; and whether, as some suggest, he smoked cannabis.
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Thackeray agreed that the inscription on the playwright's tomb in Stratford-upon-Avon betrays his phobia of exhumation.
The inscription on his gravestone reads: "Good frend for Jesus sake forebeare/ to digg the dust encloased heare/ blese be the man that spares thes stones/ and curst be he that moves my bones."
The stern inscription on the slab has been at least partially responsible for the fact that there have been no successful projects to open up the grave, according to Professor Philip Schwyzer at Exeter University.
Thackeray believes that Shakespeare's curse on gravediggers can be avoided.
"We could possibly get around that by at least exposing the bones and doing high-resolution non-destructive laser surface scanning for forensic analyses, without moving a single bone," he said.
He also said that, since there were no known verified portraits of Shakespeare, laser-scanning could help to produce a reconstruction of his face.
Other historians backed Thackeray's call. Stanley Wells, honorary president of the Shakespeare Birthplace Trust and editor of the Oxford and Penguin Shakespeares, said that he was in favour of any rational investigation to discover more about the playwright.
The successful exhumation and reburial of Richard III began with the discovery of his grave beneath a car par in Leicester in 2012. His remains have been reinterred at Leicester Cathedral last week.
Analysis of Richard III's remains have established much about his life. It is now known that he suffered from spinal abnormalities and died after a crushing blow to the head.