If carried out, the execution would have been the state’s first in nearly 12 years.
Arkansas Governor Asa Hutchinson said he is "disappointed in this delay for the victim’s family."
"While this has been an exhausting day for all involved, tomorrow we will continue to fight back on last minute appeals and efforts to block justice for the victims’ families,” the governor added.
Arkansas Attorney General Leslie Rutledge had asked the Supreme Court to allow Davis' execution to go forward. Davis' death warrant expired at 12 a.m. Tuesday.
Rutledge said it was “heartbreaking that the family of Jane Daniel has once again seen justice delayed.”
"There are five scheduled executions remaining with nothing preventing them from occurring, but I will continue to respond to any and all legal challenges brought by the prisoners," Rutledge said in a statement posted on Twitter.
"The families have waited far too long to see justice, and I will continue to make that a priority."
Davis is expected to head back to death row, even though he was already served his "last meal" on Monday. This is the second time that Davis, 54, has come within hours of execution. In 2010, he came within six hours of execution for the 1990 death of Jane Daniel.
Arkansas initially planned to execute eight convicts between Monday and April 27 as it rushes to use the state’s supply of a key lethal injection drug before it expires at the end of the month.
The state has not executed anyone since 2005.
Hundreds of people, including actor Johnny Depp and former Arkansas death row inmate Damien Echols, attended an anti-executions rally in Little Rock, Arkansas, last week.
Protesters gathered at The Rally to Stop the Arkansas Executions on Friday asking the governor to abolish the death penalty in the state.
Echols, one of the so-called West Memphis Three who was freed from prison in 2011 despite a murder conviction, said he felt it was his duty to attend the rally.
"I felt that this was my responsibility to come here and do what I can do, to do the best job I can do, to speak and do whatever I’m capable of doing to change the situation, I can't make them do anything, all I can do is say please reconsider and ask ... look what almost happened to me,” Echols told ABC affiliate KATV on Friday.
ABC News' Darren Reynolds and The Associated Press contributed to this report.