Nazanin Zaghari-Ratcliffe announces hunger strike to protest lack of medical care in Iran jail
"We are urging for an immediate action to be taken," they said in a joint letter.
Initially arrested in 2015, Mohammadi was sentenced to 10 years in prison for "forming and managing an illegal group", among other charges.
Zaghari-Ratcliffe was arrested in 2016 and is serving a five-year jail sentence for alleged sedition.
"Nazanin is currently having medical treatment blocked for lumps in her breasts, for neurological care over her neck pains and numbness in her arms and legs, and seeing an outside psychiatrist has been banned," her husband Richard Ratcliffe told AFP.
"These are all being personally blocked by the head of Evin clinic, Mr Khani, despite having been approved by the prison doctor."
Mohammadi was the spokeswoman for the now-outlawed Defenders of Human Rights Centre, which was co-founded by Nobel Peace Prize laureate Shirin Ebadi.
"We are severely disturbed and concerned by this prevention of specialist care approved by the prison doctor and strongly protest against it," Mohammadi and Zaghari-Ratcliffe said, according to the joint letter, originally published on Ebadi's website.
"In protest to this illegal, inhuman and unlawful behaviour, and to express our concerns for our health and survival at this denial of specialist treatment, despite taking daily medicines, we will go on hunger strike from January 14 to 16.
"We are urging for an immediate action to be taken.
"We announce that in the event of the authorities failure to address these concerns and them further endangering our health, we will take further actions.
"The authorities of the Islamic Republic of Iran are to be held responsible for the potential consequences."
Zaghari-Ratcliffe, who works for the Thomson Reuters Foundation - the media organisation's philanthropic arm - was arrested at Tehran airport on 3 April 2016.
She is serving a five-year jail sentence for alleged sedition.