The West Africans, who finished second in Group F behind the United States but ahead of Saudi Arabia on goal difference, will play Mexico in Incheon on Thursday.
However, the young Lions of Teranga will face the Mexicans without two key players who are suspended for the round of 16.
Centre-back Cavin Diagne was sent off right at the end of their final group match against Ecuador after picking up a second yellow card.
Fellow defender Souleymae Aw was cautioned for a second time in the tournament and is also banned for one game.
But Ibrahima N'Diaye, who sat out the Ecuador fixture after being booked in his side's first two games, will be back.
His absence was felt by coach Joseph Koto, who played for the senior national team between 1980 and 1986 and coached the side in 2012.
"We could have won and topped this group to face [one of the third placed teams], but this is what we've got. We'll take it step by step.," goalkeeper Mouhamed Mbaye, told Fifa.com
He added: "Our next game is against Mexico and we're ready to play!"
Senegal, making their second appearance in Fifa's flagship youth event, were semi-finalists on their debut in New Zealand two years ago.
Click here for U-20 World Cup results from the Fifa website
Round of 16 Fixtures:
Tuesday 30 May
Venezuela v Japan
Korea v Portugal
Wednesday 31 May
Uruguay v Saudi Arabia
England v Costa Rica
Zambia v Germany
Thursday 1 June
Mexico v Senegal
France v Italy
USA v New Zealand
The Fifa Under-20 World Cup has reached the knock-out phase in South Korea with Senegal very much in contention.