Broadcasters KBS, MBC and YTN told police their networks were halted around 14:00, Yonhap news agency said.
Two banks, Shinhan Bank and Nonghyup, said their networks were affected.
The exact cause of the problems remains unknown. Last week, North Korea accused the US and its allies of attacks on its internet servers.
The networks had been “partially or entirely crippled”, the Korean Internet Security Agency (KISA), a state watchdog, said.
“This incident is pretty massive and will take a few days to collect evidence,” a police official told AFP news agency.
Staff at the three broadcasters said their computers crashed and could not be restarted, with screens simply displaying an error message, although they have continued to make television broadcasts.
There are reports of skulls popping up on some computer screens, which could indicate that hackers had installed malicious code in the networks, KISA said.
Some banking services at Shinhan bank, including internet banking and ATM machines, were also affected, although banking operations now appear to have been restored.
A third bank, Woori Bank, also came under attack but was not infected, authorities say.
South Korean internet service provider LG Uplus said it believed its network had been hacked, Reuters news agency reported, citing an unidentified spokesman.
But AP news agency reported LG Uplus spokesman Lee Jung-hwan as saying that the company’s networks were operating normally, with no signs of a cyber-attack.
An official from the presidential office told Yonhap the authorities were “now trying to determine the cause of the network paralysis”, adding it was not yet known whether North Korea was involved.
“We do not rule out the possibility of North Korea being involved, but it’s premature to say so,” Defence Ministry spokesman Kim Min-seok said.
No government-related computer networks had been affected, an official from the National Computing and Information Agency (NCIA) told the agency.
The military has upgraded its information surveillance status by one level, Yonhap said.
North Korea is believed to have been behind two major cyber-attacks on the South in 2009 and 2011 that targeted government agencies and financial firms.
Nonghyup bank was one of the victims of the 2011 attack, which left its customers unable to access or transfer their cash for three days.
North Korea has stepped up rhetoric in recent days in response to fresh UN sanctions over its nuclear test in February and joint annual military drills between the US and South Korea, which it bitterly opposes.
Last week, North Korea’s KCNA news agency accused the US and its allies of “intensive and persistent” hacking attacks on its networks.
Official sites such as KCNA, Air Koryo and Rodong Sinmun, the party newspaper, were reportedly inaccessible for short periods.
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