Thamer al-Sabhan is the first Baghdad-based Saudi ambassador in a quarter century, but while full diplomatic relations are restored, there is still significant hostility to Riyadh in some quarters and there have already been calls for the envoy's expulsion.
The foreign ministry summoned Sabhan "to inform him of its official protest regarding his media statements that represented interference in Iraqi internal affairs," it said in a statement.
Sabhan said in interview with Al-Sumaria television that the Hashed al-Shaabi paramilitary forces, which are dominated by Iran-backed Shiite militias, are not wanted in Sunni Arab and Kurdish areas as "they are not accepted by the sons of Iraqi society".
Iraq turned to Shiite militia forces in 2014 to help counter an IS onslaught that overran large areas north and west of Baghdad, and they have played a key role in the fight against the jihadists.
But militias and their affiliates have also carried out abuses including summary executions, kidnappings and destruction of property, and many members of the Sunni Arab and Kurdish minorities view them with suspicion.
The foreign ministry defended the Hashed al-Shaabi, "which is fighting terrorism and defending the sovereignty of the country, and works under the umbrella of the state."
Shiite politicians had earlier reacted angrily to the Saudi ambassador's comments, but the country's largest Sunni bloc defended him.
"The remarks of the Saudi ambassador indicate clear hostility and blatant interference in Iraqi affairs," Khalaf Abdulsamad, the head of the Dawa parliamentary list, said in a statement.
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- 'Major insult' -
"His talking about the Hashed al-Shaabi in this way is considered a major insult," Abdulsamad said, calling on the foreign ministry to "preserve the dignity of the Iraqi state and summon the Saudi ambassador and expel him from Iraq."
Alia Nasayif, an MP from the State of Law bloc, said the ambassador's remarks "included clear attempts to provoke sectarian strife".
And Hashed al-Shaabi spokesman Ahmed al-Assadi termed Sabhan an "ambassador of a state that supports terrorism" and called for Iraq to "expel this ambassador and punish him for his statements."
Among Iraqi Shiites, Saudi Arabia is widely viewed as a supporter of extremists and opponent of their community.
But Sabhan's comments were not universally panned, with the Alliance of Iraqi Forces, the main Sunni Arab bloc in parliament, describing his remarks as "very natural" and criticising the "political campaign" against him.
Sabhan's tenure in Iraq, which officially began when he presented his credentials 10 days ago, was off to a rocky start even before his recent remarks.
Saudi Arabia's execution of activist and Shiite cleric Nimr al-Nimr at the beginning of the month sparked widespread anti-Riyadh anger, protests and calls for Sabhan to be kicked out of Iraq.
Iraq has been plagued by years of tensions between its Shiite majority and Sunni minority, which ruled the country under Saddam Hussein, with tens of thousands killed in sectarian violence over the past decade.
The United Nations said last week that more than 18,000 Iraqi civilians had been killed in the previous two years, many due to an upsurge in violence with the rise of IS.