Mothers and Newborns Health Insurance Act of 1999 - Amends title XXI (Children's Health Insurance) (CHIP) of the Social Security Act (SSA) to give States, subject to specified guidelines, the authority to provide for: (1) optional coverage of pregnancy-related assistance for targeted low-income pregnant women under the State's CHIP plan; and (2) automatic eligibility and enrollment for child health assistance under the State's CHIP plan for children born to targeted low-income pregnant women receiving such pregnancy-related assistance when the child is born until the child attains one year of age.

Amends title XIX (Medicaid) of the Social Security Act (SSA) with respect to the transitional increased Federal matching rate for increased administrative costs related to Medicaid-eligibility determinations of individuals receiving aid or assistance under SSA title IV part A (Temporary Assistance for Needy Families) (TANF). Removes Medicaid- eligibility determinations with regard to TANF recipients from such provisions. Repeals the termination of authorization for the increased Federal matching rate. Includes as administrative expenditures those attributable to the administrative costs of CHIP-eligibility determinations with regard to children and pregnant women and outreach to such populations likely to be eligible for such benefits. Directs the Secretary of Health and Human Services to establish a procedure under which, if a State does not obligate available amounts, local and community-based organizations in CHIP and Medicaid, with State approval, may seek to have administrative costs relating to outreach and enrollment of children and pregnant women treated as State administrative costs.