The 32-year-old announced the new arrival on Twitter, posting: “Today, our daugher was born. Love, gratitude and joy fills our hearts. She is fantastically cute! And we're all doing well.”
Lööf has not yet revealed the name of the baby, whose father is the Centre Party leader's husband Carl-Johan Lööf.
When publically announcing she was pregnant in April she told Swedish media that she was set to take six months of parental leave.
But she added that she would still do “certain things that party leaders do during that time” such as making a Christmas speech.
The Centre Party has said that Anders W. Jonsson, an MP and former doctor in his fifties, will take over most of her duties including party leadership debates.
In Sweden, parents are entitled to 480 days of paid parental leave and her husband, whom she married in 2011 is also expected to take several months off work.
Lööf has made no secret of her desire to become a parent.
In an interview with Swedish newspaper Aftonbladet in 2012 she said: “Someone asked what title I was hoping for after 2014 [an election year in Sweden] and I answered 'mum'. It would be great”.
Lööf became MP for Jönköping County in southern Sweden when she was just 23 years old. She followed her father Hans-Göran Johansson’s footsteps into politics; he is also a Centre Party politician and is the current mayor of Värnamo Municipality. She was selected to become leader of the party in 2011.
The Centre Party has rural roots and agricultural and environmental issues remain key concerns although the party has tried to attract urban voters by promising help for small businesses.
Lööf's baby is not the first to be born to the leader of a major Swedish political party in 2015.
In May the new head of the centre-right Christian Democrats, Ebba Busch Thor, gave birth at the age of 28 having been selected to lead her party while pregnant.
Sweden has a higher proportion of women in parliament than anywhere else in Europe (around 44 percent) although it has never had a female prime minister.