"You know what, when the Yankees want to announce something, [we will]," Cashman told ESPN New York. "Alex should just shut the f--- up. That's it. I'm going to call Alex now."
Rodriguez tweeted Tuesday that he has been cleared to play in rehab games. Rodriguez's comments seemed to contradict what Cashman told ESPN New York's Wallace Matthews on Monday.
"Visit from Dr. [Bryan] Kelly over the weekend, who gave me the best news - the green light to play games again!" Rodriguez tweeted.
Rodriguez, in a statement released Wednesday morning though a spokesman, said "the tweet was pure excitement" over the doctor's prognosis.
"I will continue to work hard until my efforts get me back in pinstripes and help my team win," Rodriguez said.
Cashman had on Monday shot down a report that Rodriguez had been given the go-ahead to play in games.
"He has not been cleared by our doctors to play in rehab games yet," he said. "He's getting closer. There's no doubt about it. But we don't have a date for him to start playing games yet. It could be July 1. It could also be July 5 or maybe June 25."
Cashman explained that Dr. Kelly had no jurisdiction over Rodriguez's rehab once the third baseman left New York to go to Tampa. Dr. Kelly had been approved by the team to perform the surgery and oversee Rodriguez's recovery in New York. It was now sole in the team's hands.
"There is always a chain of command with injuries," Yankees manager Joe Giardi said after the Yankees' 5-3 win on Tuesday. "And there has to be. That is the process. It goes through our training staff, our doctors, our GM and then it probably gets to me."
Girardi said he always understood that Yankees' team doctors needed to clear Rodriguez before he could play in a rehab game.
Cashman ended up emailing Rodriguez and did not get an immediate response.
The Yankees' relationship with Rodriguez has been tense since the end of the 2012 playoffs.
Team officials were aware that Rodriguez asked for a woman's phone number in the stands during Game 1 of an ALCS loss to the Detroit Tigers. Rodriguez was pinch-hit for and benched throughout the playoffs.
Rodriguez, 37, is among the names who have appeared in several documents in MLB's investigation into Anthony Bosch, the head of the Biogenesis lab that has been accused of distributing performance-enhancing drugs to players.
"Outside the Lines" has reported that baseball might seek to ban Rodriguez for 100 games, even though he technically would be a first-time offender. The Yankees owe Rodriguez more than $100 million, plus possible bonuses, for a contract through 2017.
Information from ESPN.com's Darren Rovell was used in this report.