The state originally planned to execute eight inmates, but two had previously been blocked by state and federal courts.
Unprecedented plans by Arkansas to execute eight death row inmates in 11-days have been blocked by a federal judge.
Baker's injunction follows two other court rulings this week that put a snag in Arkansas Gov. Asa Hutchinson's whirlwind race to use prescription drugs for executions that not even the pharmaceutical companies that make them support.
A stay of execution had already been granted to Bruce Ward, an inmate who was due to be executed on Monday.
The courts seem to be lining up to disagree with the governor.
"We are grateful that the Arkansas Supreme Court has issued a stay of execution for Bruce Ward so that they may consider the serious questions presented about his sanity", Scott Braden, an assistant federal public defender representing Ward, said in a statement. Solomon Graves, a spokesperson for the Department of Corrections, told CNN that the state's supply of potassium chloride expired recently (although Hutchinson's spokesperson said the state would have no difficulty acquiring more) while the supply of Midazolam is set to expire in April.
Executions in the USA 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.
"If midazolam does not adequately anesthetize plaintiffs, or if their executions are 'botched, ' they will suffer severe pain before they die", Baker wrote in her order Saturday.
If the attorney had to rush out to file an emergency petition, it would deprive the inmate of a lawyer to witness the execution, Baker said.
A state judge in Arkansas effectively stopped the executions Friday night, citing concerns over the lethal injection method. Attending the rally were actor Johnny Depp and his friend Damien Nichols, who was wrongly convicted of the 1993 killing of three boys in West Memphis, Arkansas, and spent 18 years in prison before being released on an Alford plea.
And he suggested that Arkansas should face no retaliation over his accelerated execution plan because it was hardly at the forefront of states practicing capital punishment.
Read Baker's entire ruling here. The state said it would return the drug, McKesson said, and the company issued a refund, but the drug was never returned.
Arkansas has drawn national scrutiny and criticism since scheduling its executions, which would be the state's first since 2005.
Judge Griffen said he needed time to study a request from drug distributor McKesson Corporation for the drug's use to be banned in state executions.
The supplier of the drug, McKesson Medical-Surgical, argued the medication wasn't meant to be used for capital punishment.
On Friday, Arkansas Circuit Court Judge Wendell Griffen, an outspoken opponent of capital punishment, issued an order on Friday blocking the state from using vecuronium bromide after a petition from its maker, McKesson Medical-Surgical Inc.
If Ward's stay remains in place and he is not executed this month, Arkansas would be looking at executing six inmates in 11 days - no longer an unprecedented time-frame, but one that has not been seen in this country in almost two decades.
A spokesman for Arkansas Attorney General Leslie Rutledge (R) said Friday evening that she was weighing how to respond to the stay.
The motion for a preliminary injunction was just one of many challenges the inmates have filed to halt the executions, the AP reported.