The incident took place under Yellareddypet police station limits, nearly 70 kms from here, in the wee hours, police said.
According to police, Alle Raju (28) was unemployed and this often led to quarrels with his wife Latha (25).
Last night, after a heated exchange of words between the two, Raju attacked Latha and his one-and-half-year old daughter Srilekha with an axe, killing them on the spot, they said.
The accused escaped from the scene soon after the incident, and searches are on to nab him, police added.