In a three-page letter to the foreign ministry dated February 2, the Colombian embassy expressed "serious concern", saying the eatery was paying tribute to the "worst criminal in the history of Colombia".
"The Embassy of the Republic of Colombia wants to share some information to refresh the horror that this criminal caused in Colombia... not to mention the drug addiction he promoted and the war he declared," the letter said.
"If the idea of the owner was to make his or her business look profitable and trendy, it is inducing... confusion, because Colombia is not what 'Narcos-Netflix' portrays anymore."
It said Colombia cannot "tolerate any more tributes to that criminal."
When AFP visited the restaurant in the heart of Singapore's business district Tuesday evening, patrons occupied about a dozen tables having post-work drinks, seemingly unaware of the controversy.
Several bouquets stood on stands by the door next to a decal of Escobar's face, congratulating the eatery on its recent opening.
Owner Stan Sri Ganesh told AFP that he decided on the name "simply because it had the word 'bar' in it".
Several users have posted abusive comments and sent threatening messages to the gastropub's Facebook page, he said.
"It was meant to be a pun... we never expected the abuse."
More than two decades after police shot Escobar dead in his stronghold of Medellin, the cocaine cartel leader was immortalised in the hit Netflix series "Narcos".
Escobar is still deeply popular in Medellin, where he is regarded as a saint and anti-hero -- souvenirs with his face on them do brisk business.
Colombia has recently come out of a decades-long civil conflict fuelled by drug trafficking that claimed thousands of lives.
The United Nations ranks Colombia as the world's biggest producer of coca, the raw material for the drug.
Affluent Singapore takes a strong stance against drugs, with traffickers punishable by death.
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