If you are under high risk restrictions that affect your ability to do the job, they need to know that (though they don't need to know why).
If you are going to need time off for appointments especially those that have already been scheduled in the near future then it is definitely important to tell a new employer about that.
Otherwise it is not necessary to spread the word about your pregnancy right away - but remember that it isn't something you can keep a secret forever, and it's best if management/HR hears about it from you instead of the rumor mill.
I don't have any plan to tell my boss at the job I just got. Its a super good job I'm waiting until after my probation period there to tell them.
I didn't say anything, everyone found out because a girl who worked with me knew I was. Bit no one seemed to believe her or me because I'm hardly showing and I'm 7months 1week!!
I didn't tell them until I was there a month. My supervisor told me to not tell anyone so no one at work found out besides her until I was 7 months.
No, you are under no obligation to tell them of anything health related.