Mr Juncker, 63, was
filmed by news agency AP struggling to keep his balance before a gala dinner in Brussels, Belgium.
This is not the first time he has been filmed unsteady on his feet.
The former prime minister of Luxembourg has previously blamed sciatica, which can cause numbness in the legs.
Pictures taken the same night show Mr Juncker being brought into the dinner in a wheelchair.
According to VRT, Dutch Prime Minister Rutte, one of the leaders seen supporting Mr Juncker, told reporters he was unaware of any "serious health problems" but said he was aware the 63-year-old had "had a back problem for a while".
A European Commission spokeswoman said she would not comment on personal health issues.
At the start of a speech to the Irish parliament last month Mr Juncker blamed his rather wobbly steps on sciatica.
"I have some difficulties to walk. I am not drunk. I have sciatica. I would prefer to be drunk. Hah!"
The UK's NHS website says sciatica symptoms can include pain, numbness or tingling in the buttocks, legs and feet. It is caused by compression or irritation of the sciatic nerve.