The Pakistan Meteorological Department (PMD) classified the threat as 'extremely severe cyclonic storm', on Monday.
Meanwhile, Chief Minister Sindh Murad Ali Shah took an aerial view of the city and expressed fears of a cloudburst.
According to Shah, an evacuation is underway from the high-risk areas to keep the residents of the areas safe.
Advisory
In the latest advisory, the Pakistan Meteorological Department (PMD) said that the cyclone had "moved further northward during the last 12 hours", and is now some 600km south of Karachi, 580km south of Thatta and 710km southeast of Ormara.
It added that the current system of the storm is "most likely to track further northward until the morning of June 14".
The authority also said that the cyclone was on course to cross the area between Pakistan's Keti Bandar and Indian Gujarat on June 15.
'Stay alert'
The National Disaster Management Authority (NDMA) has urged citizens to take the necessary precaution in view of the evolving situation and the potential impact of the approaching storm.
The federal authority called upon public to keep a safe distance from the shorelines, and said the cyclone would likely intensify within the next 24 hours.
"The cyclone is expected to impact southern and south-east parts of Sindh on June 13," NDMA tweeted.
Further precautions
The Civil Aviation Authority (CAA) airside department has also raised the alarm and taken precautionary measures such as mooring of parked light aircraft or re-parking to a safer place.
Earlier, Minister for Climate Change and Environmental Coordination Sherry Rehman advised all relevant departments of Sindh and Balochistan to be on 'high alert'.
"All departments in Sindh and Balochistan should be on high alert. Biparjoy Cyclone is unpredictable yet categorised as high intensity," Rehman said in a tweet.
"Panic is counterproductive but caution and planning are better than being caught unawares," she said.