The BNP chairperson was taken to the coronary care unit (CCU) of the hospital at around 3:20am, he added.
Zahid, however, declined to elaborate on her illness.
Khaleda Zia left her Gulshan residence for the hospital at around 2:55am and was admitted there at around 3:15 am, said BNP media wing member Sayrul Kabir Khan.
Visiting the party chief at 4:30am, BNP secretary general Mirza Fakhrul Islam Alamgir said physicians found her with some cardiac complications.
"Madam's condition is stable now. How complicated her problem is can be confirmed after she undergoes different tests, especially an angiogram," he said.
A medical board will analyse Khaleda Zia's health condition and reports at 10:30am on Saturday and decide the next course of treatment, Fakhrul added.
He hoped that Khaleda would recover as she did in the past. He also urged the countrymen to pray for her speedy recovery.
The BNP chairperson last went to Evercare hospital on 6 April for health check-ups.
Khaleda Zia, a former prime minister, has been suffering from various ailments, including liver cirrhosis, arthritis, diabetes, kidney, lung and eye problems.
The 76-year-old was last admitted to Evercare on 13 November last year where she was diagnosed with liver cirrhosis.
On 1 February, Khaleda Zia returned home after an 81-day stay at the hospital as she was suffering from internal bleeding caused by liver cirrhosis.
The former prime minister was sent to the Old Dhaka Central Jail as a lower court sentenced her to five years' imprisonment in the Zia Orphanage Trust graft case on 8 February, 2018.
Later, she was found guilty in another corruption case the same year.
Amid the Covid-19 pandemic, the government temporarily freed Khaleda Zia from jail through an executive order suspending her sentence on 25 March, 2020, with conditions that she will stay at her Gulshan home and not leave the country.