After their engine failed and their anchor was lost off the coast of India's Andhra Pradesh state in June last year, the men were left stranded in dangerous waters.
They drifted helplessly for a week in the Bay of Bengal until an oil tanker under the command of Capt Menon came to their rescue.
Her efforts have now been recognised with the International Maritime Organization's (IMO) Award for Exceptional Bravery at Sea, handed out in London on Monday.
Not only is Capt Menon the first female captain in the Indian Merchant Navy, but she is the only woman to have won the award, which recognises those who risk their own lives to save others at sea.
As waves rose to 9m and wind speed reached 60-70 knots, she commanded a rescue operation last June that required three attempts to get the fishermen onboard the massive tanker via a pilot ladder from their small boat.
The Sampurna Swarajya tanker's second officer had earlier spotted the fishing boat 2.5km away off the coast of Gopalpur in Orissa. The men had been surviving off ice from their cold storage after food and drinking supplies were washed away.
"The sea was very, very turbulent, there was a depression... which was stagnant for two or three days and it had intensified into a deep depression," Capt Menon told BBC World News TV.
"It was a very difficult task but we had to do it because if I didn't do that I was knowing very well that these fishermen never stood a chance of rescue, no survival at all."
As far as being a path-breaking female ship captain goes, Radhika Menon doesn't appear to make a big deal of it. She says gender means little on the kind of ships she works on.
"[It is] gender neutral in the sense that even if you are female, you know how to do your job," she says.
"People appreciate you, they respect you, you'll be able to carry out your orders and all that."

The Blue singer, who is in the final of the BBC One competition, said it began after a short tour of Kazakhstan ended in July.
"I was a bit gutted at first because the music went quiet," he told Newsbeat.
"I didn't have an outlet so I was sitting at home and got myself into a bit of depression."
He said he realised the fans could tell he wasn't feeling himself and thought that he needed to tell them.
"Hopefully I've done that and now I am just so grateful for this Strictly team," he said.
"Even though I have been in a dance-off, they picked me up just before I went out there and danced.
"I remember it being an absolute saviour and I can't thank them enough."
In an interview with the Daily Mirror earlier this year, he revealed how he had turned to alcohol after Blue's reunion tour finished.
He also admitted property losses had led him to bankruptcy and he even thought about suicide.
The Strictly finalist said it was then that he realised he was suffering from severe depression.
But since appearing on the show, he says he feels things are looking more positive and he is looking towards the year ahead.
"Career-wise we've got two albums with Blue next year, we're signed to Sony," he explained.
"We've got our own TV show as well which is going to be launched in January, so things are looking very, very good for Blue next year."
He will also go on tour with this year's Strictly Come Dancing contestants and could potentially win on Saturday night with dance partner Kristina Rihanoff.
"What a great way to end the year, it didn't start off too well but I feel I ended on a high no matter what."
Strictly Come Dancing final is on BBC One at 18:30 on Saturday.
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Seven fishermen owe Captain Radhika Menon their lives.
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Simon Webbe has credited Strictly Come Dancing with helping him with his depression.