Swift is in hospital where he will undergo an MRI scan after a crash on the final descent of the 169.8km race from Alcudia to Playa de Muro.
His Team Sky team-mate Wiggins had earlier pulled out 100km from the finish, but was apparently uninjured.
Wiggins is easing into his season on the Balearic Islands and finished 161st and 152nd out of 178 riders in the two previous races.
Orica-GreenEdge rider Howard came through to clinch victory in the final instalment of the four-day Challenge Mallorca.
Maarten Wynants of Belgium was second, with Italy’s Davide Cimolai taking third spot.
Egoitz Garcia Echeguibel of Spain was fourth, while compatriot Jose Joaquin Rojas completed the top five.