Luton confirmed it was a Hatters fan who had suffered the emergency and they are now in a stable condition.
A Luton statement read: "We are relieved to report that the Luton Town supporter who fell ill in the Kenilworth Road stand is in a stable condition and is on his way to hospital.
"Once again, our thoughts are with him and we all hope he makes a speedy recovery."
Rob Edwards' side went into the clash looking to avoid a third-straight defeat having lost to Leeds United and Norwich City in their previous Championship fixtures.
As for Swansea, they are hoping to get back to winning ways after a 2-2 draw with Portsmouth last Saturday.
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The health scare at Kenilworth Road comes two weeks after Millwall and Sunderland's Championship game had to be suspended due to multiple medical emergencies.
Sunderland took the lead through Aaron Connolly after just 10 minutes but the contest was halted in the closing moments of the opening half.
Millwall's Ryan Leonard went to take a throw-in but immediately called for medical assistance.
There were subsequently two separate medical emergencies reported in the Millwall end, while a third occurred among Sunderland's travelling supporters.
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Medical staff from both clubs rushed over to assist before the players departed the field at The Den.
Millwall posted: "The players have left the pitch following a medical emergency in the crowd. We send our best wishes to those receiving attention."
Sunderland shared a similar statement: "Play has been temporarily suspended due to a medical emergency at The Den."
The contest resumed after a delay of 30 minutes and ultimately finished 1-1 as Femi Azeez's strike rescued a point for the hosts.