The scrum-half suffered the injury in an off-the-ball incident during the first half at the Liberty Stadium, leaving the field immediately.
X-rays over the weekend confirmed that initial fears of damage to the eye socket were unfounded, but the nose break was confirmed.
Head Physio, Chris Towers, said:
"Rhys suffered a depressed fracture of the nose. Over the last few days we've sought out expert medical opinion, and he's been cleared as fit to continue playing."
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