According to a statement by the ECB, the decision was taken following scanning and subsequent consultant reviewing since the pacer returned to the UK on Tuesday.
Archer had also taken an injection for the right elbow injury that had deemed him unfit for selection for the ongoing ODI series against India.
"The procedure on Jofra’s hand will take place on March 29 so that he recovers during the planned break following his elbow injection. Jofra suffered a cut to his hand while cleaning at his home in January shortly before flying to India to prepare for the Test series. The injury was managed by the ECB’s medical team through the tour and it did not impact on his availability," the ECB said in a statement.
"Further investigation and a specialist opinion was sought upon his return to the UK and, in conjunction with the ECB medical panel, it has been decided that surgery is the best option to manage his injury in the longer term. Further detail will be provided in due course," it added.