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Video circulating on Twitter appears to show an oxygen tank being delivered to the High Commission in New Delhi, before it is carried inside the commission gates.
India is battling a devastating onslaught of the virus that is killing thousands of people each day.
The outbreak has crippled the country's medical system, with severe shortages of supplies, including oxygen tanks.
The High Commission today originally tweeted to the Indian Youth Congress and its national president Srinivas BV: "Could you please help with oxygen cylinder urgently at the New Zealand High Commission? Thank you."
Srinivas BV responded promptly, saying they would come to assist.
Shortly after he tweeted photos of a team with oxygen tanks, saying: "We have reached New Zealand High Commission with oxygen cylinders".
The tweets have garnered a huge amount of attention, with thousands of retweets and comments in less than an hour.
The High Commission's tweet was then deleted, and replaced with: "We are trying all sources to arrange for oxygen cylinders urgently and our appeal has unfortunately been misinterpreted, for which we are sorry."
Srinivas BV later posted video of the oxygen being delivered and tweeted: "Update- New Zealand High Commission opened gates of the embassy and accepted cylinders.
"Also, they thanked the #SOSIYC team for this quick relief as patient inside embassy was critically ill."
The Herald sought comment from the Ministry of Foreign Affairs and Trade, and Foreign Affairs Minister Nanaia Mahuta on why oxygen was apparently delivered to the High Commission, whether there is a critically ill patient inside, and whether it's appropriate for diplomats to use social media to seek medical supplies given the gravity of the Covid crisis in India.
An Mfat spokesman said the tweet was issued "in error" on the High Commission's Twitter account.
"It has since been withdrawn and we have apologised, including to the Indian government, for the misunderstanding it may have caused. We have nothing further to add except to say that the safety, health and welfare of our staff in India and across the global network is a priority."
Indian media are now reporting the incident.
NDTV.com said following the tweet, India's Ministry of External Affairs had advised foreign missions "not to hoard essential supplies, including oxygen".
"The Chief of Protocol and Heads of Divisions are in continuous touch with all High Commissions, Embassies and MEA is responding to their medical demands, especially those related to Covid. This includes facilitating their hospital treatment. Given the pandemic situation, all are urged not to hoard essential supplies, including oxygen," the ministry said.
NDTV.com reported that the New Zealand High Commission's SOS for oxygen followed a similar appeal by the embassy of the Philippines yesterday.
Some commentators are now speculating whether the New Zealand mission was "coerced" into deleting its tweet because it was embarrassing for the Indian government.
India set yet another daily global record with 401,993 new cases, taking its tally to more than 19.1 million.
Another 3523 people died in the past 24 hours, raising the overall fatalities to 211,853, according to the Health Ministry. Experts believe both figures are an undercount.
Last week, Mahuta announced New Zealand was providing $1m to the International Federation of the Red Cross to assist India while they responded to the current surge in Covid-19 cases.
This included providing oxygen cylinders, oxygen concentrators, and other medical supplies.