This rate should apply to workers of all ages, instead of the current lower rate for under-23s, it said.
Minimum wage is £9.50 an hour for workers over the age of 23 and £9.18 for 21 and 22 year olds. Inflation - the rate at which prices rise - is at 10.1% - so wages do not go as far.
The government said raising the minimum wage could push unemployment up.
Prices are rising at their fastest rate in 40 years, driven by higher food, fuel and energy costs.
Frances O'Grady, general secretary of the TUC, said: "Every worker should be able to afford a decent standard of living.
"But millions of low-paid workers live wage packet to wage packet, struggling to get by - and they are now being pushed to the brink by eye-watering bills and soaring prices."
The government said it was "determined to make work pay" and that this year's increase in the minimum wage, in April, was the largest ever rise. However, it said setting the minimum wage too high or increasing it too quickly could lead to higher unemployment.
The TUC argues that at a time when companies are paying increased dividends to shareholders, the government should ensure workers get "their fair share" by increasing minimum wage rates now, rather than waiting for the next expected uprating in April.
It should start with low-paid workers who are "absolutely terrified about what those hikes in energy bills will mean for their budgets, having to fork out for school uniforms and put food on the table", Ms O'Grady told BBC Radio 4's Today programme.
She said a higher minimum wage would mean workers were less likely to be claiming in-work benefits, and more likely to be paying taxes as well as buying goods and services on the High Street.
Kelly, 31, works front of house in a well-known London restaurant and despite eight years of experience in the sector is paid the minimum wage. Her income is topped up with tips and her partner has a salary, but she has still seen a decline in her quality of life over the past decade.
"We are constantly in a precarious position, living hand-to-mouth," she said. "[We're] being squeezed further and further."
But Mark Hodges, 66, who runs a clubhouse restaurant on a holiday park in Norfolk, said raising the minimum wage to £15 an hour would mean restaurants would have to raise prices.
"Although it would be fantastic to see us all move to £15 an hour, I cannot see how such a large rise - across all ages - would do our sector many favours," he said.
"If somebody said let's move to £15 an hour by 2027 so the industry had plenty of time to plan and adjust, then maybe it's achievable," he told the BBC, but he wouldn't like to see the minimum wage go up immediately at a time when everything else is rocketing in price.
And giving the same minimum wage across the board, would mean older workers applying for jobs that are currently given to younger, less experienced workers.
"The people who would suffer would be young ones," he added.
Before the minimum wage was first introduced in 1999 some economists warned it could lead to job losses because firms would hire fewer people. But there has been no evidence of overall job losses linked to the minimum wage.
The TUC said the evidence from around the world suggested higher minimum wages led to higher wages overall, rather than job losses.
There was no justification for paying lower rates to younger workers, Ms O'Grady added. Workers aged 18 to 20 are paid a minimum of £6.83 an hour.
"It's clear to me, and I think to many people, that people ought to be paid the rate for the job, regardless of the age they are," Ms O'Grady said.
"If they're working as hard doing the same job, why should they be discriminated against simply because they're under 23?"
However, Matthew Percival, director of skills and inclusion at the CBI, which represents businesses, said there should not be a new target for the minimum wage and that any rise in its rate should be rooted in growth and higher productivity across the economy.
"Firms are increasing wages where they can, but energy price rises are pushing some to the brink. High energy prices require urgent government action to support households and businesses, not relying on the minimum wage alone," he said.
The minimum wage is set in relation to the median wage - an average calculated by taking every pay packet in the UK and identifying the mid-point. The current target is for the minimum wage to reach 66% of median wages by 2024. The TUC argues wages should rise for all workers to an average of £20 an hour and that the minimum wage target should be 75% of that.