Messi, 26, was sick on the pitch during Argentina's midweek friendly against Romania, and has been reported to have thrown up in other matches for his country and Barcelona previously.
When asked about the subject on Friday, Martino admitted the bouts of vomiting were "not normal" but played down the seriousness, adding that the issue has not been affecting the four-time World Player of the Year's ability to perform.
"I've spoken with him and it happens regularly. I'm not a specialist but I understand it's not something normal," Martino said ahead of this weekend's Primera Division trip to Real Valladolid.
"He's even been to see specialists at certain times and a solution hasn't been found yet, but there's no cause for concern It doesn't affect him doing his work at all. It's something he's had for some time."
Martino also heaped praise on "irreplaceable" defender Carles Puyol following the centre-back's decision to leave the Catalan giants.
Puyol, 35, announced earlier this week that he would bid farewell to Barca at the end of the season after 19 years at the club in which he has made 593 first-team appearances - second only to current team-mate Xavi in the club's history - and helped them win 21 trophies.
Martino said: "I think he's a footballer who is irreplaceable. I'm probably not the best-placed person to comment on this, because I've only worked with him for seven or eight months, but that's enough to say what I said.
"He's the type of player that a club has only once every so often. Life goes on at Barcelona, and the club will look for a replacement, but he'll always be in everyone's heads because he leaves an indelible mark."
Puyol admits he does not know what his next step will be - save to take a bit of a break in the summer - but Martino has played down suggestions that the centre-back, who has won 100 caps for Spain, might immediately try his hand at football management.
"It's not that I don't see him as a coach, I've thought that he could, but he told me he's not looking there, at least now," Martino said.