The video, taken during Tsipras' visit to the European Parliament on Wednesday, shows Podemos party leader and MEP Iglesias standing in a row of people waiting to shake hands with the Greek prime minister.
As Iglesias places one hand on Tsipras' shoulder and extends the other, ready for a hand-shake, Tsipras seemingly overlooks him to greet French MEP Jean-Luc Mélenchon.
The Vine has been shared thousands of times across social media sites Twitter and Facebook with commenters saying that Tsipras was haciendo la cobra, or making like a cobra, meaning he ducked away from Iglesias like a snake to avoid greeting him.
A YouTube video of the same scene shows more clearly Tsipras shaking hands with the people before Iglesias and then skipping over the Podemos politician for Mélenchon.
Whether Tsipras intentionally snubbed Iglesias is not known.
Iglesias and his Podemos party had backed the 'no' vote supported by Tsipras in a Greek referendum last Sunday, which resulted in 61 percent voting 'no' to an offer by the country's European creditors for more budget cuts.
Iglesias hailed the referendum results as a victory for "democracy".
Podemos has been an ally of Tsipras' left-wing Syriza party, both driven by opposition to austerity measures.
Tsipras has until Thursday make new proposals for agreements on a third bailout programme with its European creditors, or it faces and exit from the eurozone.