Smith's X-ray scans showed there was no bone fracture, and he will be examined closely ahead of the second ODI on Sunday.
"Smith's X-ray scans show there are no new fractures to his left hand, only soft tissue swelling and bony contusion. He is under the care of the physiotherapist and we will reassess his injury in the next day or two," commented team manager Mohammed Moosajee.
Jacques Kallis, who was carried off the field because of severe cramping will also be monitored closely in the next 24 hours.
"Kallis had to be connected to an intravenous line after suffering from dehydration on the field. He was recovering from a viral infection which triggered his initial bout of nausea and dizziness, which led to the severe dehydration and cramping."