Do you have a custody order or parenting agreement? What does it say about travel? How old is the child and which country is the child going to? Does the child have a passport?
You should go to the U.S. Department of State website and search for the country you plan to visit. On the country’s page you can find out what that country requires for a minor child to enter the country. Different countries have different laws. For example, Canada, requires that each child traveling with only on parent or guardian have a passport, birth certificate, a custody order from the court (if there is one) and recommends a letter of authorization signed by the parent who is not traveling.
For a child under 16 to get a passport, both parents have to give permission. You can block your ex-spouse from getting a passport for your child by filing a request with the U.S. Department of State through the Children’s Passport Issuance Alert Program (CPIAP). If you file a request with CPIAP the State Department will notify you when they receive a passport application for your child. They will follow up to confirm that you give your permission for your child to get a passport.
If there is no custody order in place about international travel, you may also file an action asking the court to prohibit international travel or require the traveling parent to deposit a bond with the court to insure the return of the child, if you have evidence that the traveling parent does not intend to come back to the U.S.