Governor Charlie Baker said Tuesday the State Ethics Commission should investigate an unusual arrangement that allowed state Senator Brian Joyce to receive free dry cleaning from a Randolph shop for more than a decade.

“This is the sort of thing that certainly flies in the face of what most people would consider — if it’s borne out to be true — proper behavior,’’ Baker said on his monthly radio show on WGBH-FM.

Baker, a Republican, was referring to a Globe story published Tuesday that detailed how Joyce, a Milton Democrat, brought his suits, his family’s clothes, and sometimes his aide’s clothes to Woodlawn Cleaners after the owner, Jerry Richman, casually offered to clean his clothes for free in 1997. Richman said the arrangement lasted until he sold the business in 2008. Joyce’s attorneys insist the senator received the free dry cleaning in exchange for free or reduced-price legal services that he provided to Richman.

“The facts of that matter as they are described in that story justify a pretty quick and pretty immediate review,’’ by the Ethics Commission, Baker said. He added that the arrangement was also “an issue for the voters and for the leadership of the Senate.’’

David Giannotti, a spokesman for the State Ethics Commission, said the panel cannot, under state law, confirm or deny that it is reviewing any matter.

Baker’s remarks were notable because he often tries to avoid making public pronouncements that could anger the Democratic Legislature, which controls the fate of his legislative agenda. But in this case, he was speaking out amid a growing outcry from his allies in the GOP.

Just before he spoke Tuesday, the state Republican Party issued a statement calling on Senate President Stanley C. Rosenberg to remove Joyce from his committee posts. The Massachusetts Fiscal Alliance, a conservative group, went a step further, calling on Joyce to resign.

Joyce, in a statement released by a public relations firm, said he was “disappointed in the false accusations’’ in the Globe story.

“Over the course of many years, I provided uncompensated legal services to a small businessman and property owner who claimed an inability to pay for those services,’’ Joyce said. “Those legal services far exceeded any dry cleaning offered. It was a barter arrangement that he had not only with me, but with two other local lawyers. I provided evidence of this to the extent permitted within the constraints of attorney-client privilege but that evidence was ignored.’’

In Tuesday’s Globe, several ethics experts said that if Joyce traded legal services for dry cleaning, he should have kept records to show that he did not receive a net benefit of $50 or more; public officials are generally not allowed to accept anything worth more than that.

Joyce has acknowledged there is no written record of the dry-cleaning-for-legal services arrangement and he cannot remember when it began. One document shows he waived $12,250 in legal fees for Richman in 2007.

Joyce stepped down as assistant majority leader last year amid ongoing investigations by both the Ethics Commission and the Office of Campaign and Political Finance for possible violations of the state’s conflict-of-interest and campaign finance laws, according to his Senate colleagues.

Those probes came after the Globe reported that Joyce obtained 40 pairs of $234 sunglasses as holiday gifts for his colleagues but didn’t pay until the Globe asked about them and that he charged his campaign fund $3,400 to pay for his son’s high school graduation party in 2014. The Globe has also reported on Joyce’s representation of a private legal client before a state agency — a possible violation of state law.

Joyce was a private lawyer for Energi, a company that sells insurance to the energy industry, and owned stock in the company when he lobbied state insurance regulators on the company’s behalf. State conflict-of-interest law prohibits public officials from using their position to advance their private business.

In his statement Tuesday, Joyce said the Ethics Commission investigated the sunglasses issue and “closed out this matter as unworthy of any further action.’’ Tara Frier, a Joyce spokeswoman, said another Joyce attorney, Howard Cooper, was notified Monday that the matter had been dismissed.

However, the ethics investigation into other matters is continuing, Frier acknowledged.

“Finally, I am awaiting final resolution of the Office of Campaign and Political Finance’s investigation which I believe is imminent,’’ Joyce said in his statement. “I look forward to publicly sharing those results as soon as I am able to do so.’’

Natasha Perez, chief of staff for Rosenberg, said the Senate would not act until all investigations are complete.

“Senate President Rosenberg referred the issue of Senator Joyce’s conduct to the State Ethics Commission last May, as requested by Senator Joyce,’’ Perez said in a statement. “Rather than deal with these matters piecemeal, it makes sense to defer to completion of the Ethics Commission and OCPF proceedings before any Senate consideration.’’

Michael Levenson can be reached at mlevenson@globe.com. Follow him on Twitter @mlevenson.