Brittany King, 18, and her daughter Cheyanne were reported missing by family members on June 15, police spokeswoman Liz Wylie said.
King has been in contact with her mother and has said she is in the Petaluma area. The two have also been spotted in Milpitas.
King is unwilling to return home, and authorities believe she and her daughter are homeless, bouncing from couch to couch at friends' or acquaintances' homes.
"We are not very worried about Brittany, she is an adult, but the baby seems to have health problems, possibly bronchitis, and needs medical attention," Wylie said.
"We are hoping that someone reports their whereabouts, or Brittany contacts us, so we can get her the medical resources she needs," she said.
Wylie added that, with the heat and poor air quality that have blanketed the region the past few days, the baby's condition may have worsened.
"We just want to make sure that they're not living on the streets," Wylie said.
Anyone with any information regarding the two is asked to contact the Mountain View Police Department at (650) 903-6395.