Executions in the U.S. have fallen steadily for years, hitting their lowest level in 2016 - partly because the drugs used in lethal injection have become so hard to obtain.
Three Arkansas justices dissented, with Associate Justice Shawn Womack writing that Ward and Davis "had their day in court, the jury spoke, and decades of appeals have occurred".
Hutchinson put the execution spree into play because one of the drugs used for executions, Midazolam, is set to expire at the end of April, the BBC reports.
The injunction represents the latest legal setback in Arkansas' attempt to execute the inmates - eight of whom were originally set to be put to death by the end of April.
A different federal judge has issued a stay for an inmate who won a clemency recommendation from the state's Parole Board, while the state Supreme Court has issued one for another inmate pending more mental health tests.
Protesters gather outside the state Capitol building on Friday in Little Rock, Ark., to voice their opposition to Arkansas' seven upcoming executions. She could ask either the state court or the U.S. Supreme Court for the review.
"The unnecessarily compressed execution schedule using the risky drug midazolam denies prisoners their right to be free from the risk of torture", lawyer John C. Williams said. She said the inmates were entitled to challenge the execution process on the grounds it "creates a demonstrated risk of severe pain".
The inmates are challenging the planned execution method, and claim that the scheduling of back-to-back executions widen the probability of potential mistakes.
McKesson said it had requested Arkansas return its supply of vecuronium bromide after the San Francisco-based company learned it would be used in executions.
The company has said it sold the drug to be used for medical purposes, not executions.
On Saturday Pulaski County Circuit Court Judge Wendell Griffen was strapped to a cot, like an inmate who is set to be executed by lethal injection, about two and a half hours before he issued a temporary restraining order blocking the executions, the Washington Times reported.
Baker in Little Rock also stated in her ruling that the execution team did not have antidotes on hand in case something went wrong with the executions - a possibility, she noted, which has already happened in cases in Alabama, Arizona, Ohio, and Oklahoma when using the same drug.
In February, Gov. Asa Hutchinson scheduled the executions of eight men over an 11-day span in April. The company said it'll continue efforts to have the drug returned. "We are calling on state officials to accept the federal court's decision, cancel the frantic execution schedule, and propose a legal and humane method to carry out its executions". "Attorney General Rutledge intends to file an emergency request with the Arkansas Supreme Court to vacate the order as soon as possible". Two other pharmaceutical companies have asked a judge to prohibit Arkansas from using their drugs in the upcoming multiple executions. Supporters have said it is effective, and the U.S. Supreme Court has authorized its use. The Arkansas Parole Board had earlier voted to recommend that McGehee's death sentence be commuted to life without parole, and the judge ruled McGehee's April 27 execution date would not have given the board enough time, as required by law, to notify the governor of its recommendation.
On Friday, death row inmate Bruce Ward's execution was stayed. Baker's order comes a day after Arkansas state judge Wendell Griffen issued a broad temporary restraining order [text] in favor of the prisoners.
People, including Griffen, have been protesting outside of the Governor's Mansion in Little Rock.