Gyorgy Schopflin, a member of the right-wing government of Prime Minister Viktor Orban, sparked outrage and disbelief with the suggestion.
He made it during an ill-tempered exchange on Twitter with a human rights campaigner.
Andrew Stroehlein, European media director for Human Rights Watch, posted a tweet in which he criticised Hungary for using bizarre, totemic masks made out of beetroot to scare refugees trying to cross the border from neighbouring Serbia.
The existence of the ghoulish vegetable heads was first reported last week by a Hungarian journalist. It is not clear who made them but there has reportedly been no effort by Hungarian police or soldiers to take them down.
"Refugees are fleeing war & torture, Hungary. Your root vegetable heads will not deter them," Stroehlein wrote in his tweet.
The MEP, a former academic who is a member of the governing Fidesz party, wrote back: "Might do so. Human images are haram. But agree, pig's head would deter more effectively."
He was described as "a sad old man full of hate" and his comment was branded as "disgusting".
The pigs' head suggestion reflected a deep current of xenophobia and anti-migrant feeling within the Hungarian government, Stroehlein told the Telegraph.
"With the current government, the idea of putting up pigs' heads and turnips is in many ways the least of the issues. Their treatment of refugees has been appalling - using violence to push people back from the border. Conditions in reception centres are inhumane. Refugees are treated like animals."
Hungary closed its southern border with Serbia last year as around a million refugees and migrants, many of them from Syria, sought to travel from Turkey, through Greece and along the Balkan route to Germany and Scandinavia.
