"We are not that used to seeing babies in plenary, and in rooms where decisions are made," the Social Democrat politician said. "So therefore it's a little bit unusual today to see a baby in that situation."
She said that she had brought Uno into the chamber out of necessity rather than to make a statement.
"Even though it was not my intention that he should be photographed, I think it's important to point out that we need to be able to have politicians with babies, because we need to have poltiicians with all experiences of life. I hope it can be a role model for others."
Guteland has been bringing Uno to the parliament in Strasbourg and Brussels since September, when he was only a few months' old, and said he had so far caused few problems.
"I'm lucky in that sense. He's a quiet and calm baby normally. Sometimes he wants to speak and then he speaks loud. He doesn't cry that much, but when he speaks, people hear and notice and often laugh a bit."
But it was only after her speech on Wednesday that Uno made any impact.
Guteland is far from the first MEP to bring her baby to the European parliament. Her predecessor Åsa Westlund also brought her baby into the chamber.
Several MPs have also brought babies to the Swedish Parliament.
"I think in Sweden we are more used to see that babies can come along and go to their parents' work," she said. "Both men and women go to work and combine it with small children."
Members of the European Parliament are allowed to take six months off work after the birth of a child, but are not allowed to send a replacement, meaning their party loses a vital vote.
As a result, few MEPs take parental leave.