The formulation would be delivered via a dry powder inhaler, while it currently can only be injected.
The UK-based pharma company said inhaling would be easier to use, act more quickly and could be stored safely without refrigeration.
As part of the agreement, Vectura will receive undisclosed revenues on a fee-for-service basis.
The World Health Organisation recommends that oxytocin is administered to every woman after birth to prevent PPH, which causes 60,000 deaths each year.
It mostly occurs in the poorest and hottest countries in the world, where injections are impracticable due to a lack of cold chain distribution and sterile environments, as well as trained clinicians to administer the drug.