Emergency services were called to an address in Broadmayne near Dorchester on 27 May after the boy was found to be seriously ill.
He was taken to hospital where he was pronounced dead.
Dorset Police said a man and a woman, both aged 21 and from the Dorchester area, had been arrested.
Officers said a murder inquiry was launched following a post-mortem examination but have not revealed the cause of the toddler's death.
Insp Mike Darby said: "I appreciate the incident has impacted on this close-knit community, but it is important we understand the full circumstances surrounding the death.
"An investigation has been launched and there may be some police presence in the village while detectives carry out their investigations."
Two people have been arrested on suspicion of murder following the sudden death of a two-year-old boy from a Dorset village.