The custom for a woman after birth to not leave their home for four weeks:[1]

It is an age-old Jewish custom for women who are after birth to not leave their home for a period of four weeks from after the birth.[2] [Practically, the widespread custom today is to no longer be particular in the above, and women leave their homes as close to a week after birth.[3] Certainly, a woman may leave her home to got to the doctor, Beit Hachlamah, even within seven days.]

[1] See Admur 88:2 “If she herself has given birth in which she goes to the synagogue after four weeks, she may go even if she is a Nidah”; M”A 88:3; Shut Maharshal 58; Beis Yosef 88; Elya Raba 219:5; P”M 219 M”Z 3; Shaareiy Efraim 4:28; Birchas Habayis 27:17; Hisorerus Teshuvah 1:59; Aruch Hashulchan 219:6; M”B 219:3; Har Tzevi 1:163; Minchas Yitzchak 4:12; Divrei Yatziv E.H. 35; Betzel Hachochmah 6:78; Kinyan torah 4:22; Teshuvos Vehanhagos 1:195; Orchos Rabbeinu 1:91; Beir Moshe 8:120; Piskeiy Teshuvos 136:8; 219:10 regarding Hagomel; 239:11 regarding Shemira; Nitei Gavriel Nida Vol. 3 chapter 63:6 and 65; Shevach Habris 5:3

[2] The reason: There are several reasons behind the various parts of this custom: 1) A woman after birth is weak, and hence she would remain at home and rest for the first four weeks. [Shut Maharshal 58; Shut Bach 46] 2) A woman after birth requires Shemira, similar to a Chasan, and hence they would avoid leaving their house for a full month after birth, until the Shemira period expires. [Nitei Gavriel ibid footnote 15] 

[3] Nitei Gavriel ibid that in today’s times, on the contrary, doctors recommend a woman to leave the home after birth for the betterment of her mental health