"Archer has been recovering from right elbow surgery," an ECB statement said. "However, pushing through the discomfort whilst recently playing, hoping it will settle, has proven challenging. Therefore, it has been agreed for him to return to the UK for a period of rest and rehabilitation to give him the best opportunity for a full recovery."
Archer has played five of Mumbai's ten matches this season and has struggled to make an impact, taking two wickets and conceding 9.50 runs per over - though has regularly bowled at speeds in excess of 90mph/145kph.
He has played in four of their last five games, but will not take part in Tuesday night's game against RCB at the Wankhede Stadium or in their final three league fixtures.
Mumbai said in a statement that Archer's "recovery and fitness continues to be monitored" by the ECB's medical team. "Jofra will return home to focus on his rehabilitation," the franchise added.
Jordan, Archer's replacement, has been with the squad on standby for the last two weeks. He went unsold at December's auction but has previously played for Chennai Super Kings, Punjab Kings, RCB and Sunrisers Hyderabad, and joins for a fee of INR 2 crore (£200,000 approx.)