The 63-year-old was seen to be unsteady on his feet at the summit dinner in Brussels on Wednesday evening, and had to be helped away in a wheelchair.
The prime ministers of the Netherlands and Portugal, Mark Rutte and Antonio Costa, helped prop him up.
Commission spokesman Margaritis Schinas said it was "more than tasteless" for the press to write "insulting headlines by exploiting President Juncker's pain".
"I don't think this is elegant and I don't think this is fair," he added.
Asked whether Mr Juncker had mixed painkillers and alcohol, Mr Schinas replied: "No he didn't - at least I am not aware of this happening."
The president had suffered a "very particularly painful attack of sciatica accompanied by cramps," Mr Schinas said.
"The president has himself publicly stated that this sciatica affects his ability to walk," he continued.
"That was unfortunately the case Wednesday night.
"He is taking medication and feels better."
Sciatica occurs when the sciatic nerve, which runs from the hips to the feet, is irritated.
The German government weighed in on Friday, with spokesman Steffen Seibert saying Berlin has a "very high level of confidence" in the Commission president.
Mr Juncker, whose five-year term at the head of the commission ends next year, has faced questions before about his public demeanour.
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