Solano was scratched from the lineup on Saturday night at Philadelphia, and he has missed three straight starts.
Manager Mike Redmond said Solano has an intercostal issue.
"He's not better. He's the same," Redmond said.
Chris Valaika is filling in at second base. But the bench is thin already with Austin Kearns missing a few days because he is on the MLB bereavement list.
Green, who accepted an assignment to Triple-A New Orleans after being designated for assignment on Thursday, is batting .321 with one home run and three RBIs in eight games for Miami.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter