Salma Hayek with François Henri Pinault
and her businessman fiancé, François Henri Pinault, are the parents of a baby girl, Valentina Paloma Pinault.
"Mother and daughter are doing well," Hayek's publicist Cari Ross, said in a statement. No further details were released.
A source told PEOPLE that the 41-year-old Mexican-born actress entered the hospital on Thursday and that Pinault was present.
The daughter is the first child for Hayek. Pinault, 45, has two children from a previous marriage which ended in divorce in 2004.
The actress's pregnancy
was first revealed in March, at the same time that the couple announced they were engaged to be married.
The pair had kept a relatively low profile since their relationship began – though Hayek joined Pinault, the CEO of luxury goods firm PPR (which owns Gucci and Yves Saint Laurent), for occasional public events, including one in the spring at the festivities surrounding the inauguration of the Pinault Foundation's Modern Art collection in Venice's Gritti Palace.
Besides carrying her child, Hayek has had her hands full on Ugly Betty
, both as a guest star and as the executive producer of the Emmy-winning ABC show.
Speaking of Hayek, actor Michal Urie, who plays a conniving assistant on the series, told PEOPLE
: "She knows how to take care – like we have a ton of producers, and she's really caring. She's like the matriarch of the producers. She's already motherly."
Another Ugly Betty
star had equally glowing praise for Hayek. "She's a fighter, she's just lovely. She's like the salt of the earth and not pretentious one bit," Vanessa Williams said Emmy night. "And you get a little snippet of that when you see her character that she did a couple of episodes with, when she smacks America or Betty on the behind and she's that strong, forceful woman – she's a dynamo."
And though she is first-time mom after 40, Hayek spoke confidently
of motherhood to Marie Claire
magazine earlier this year, saying: "Motherhood is not for everyone. It is for me, but there's no reason women should feel rushed to have a child."
Who's turning 40? Which celebs are high school dropouts? What's hot and definitely not in fall fashion?
Check out PEOPLE's new digital magazine now!