Immigration New Zealand (INZ) has apologised for sending the instruction, which was an automated response.
Kharkiv is being bombarded by Russian artillery and Kyiv remained under siege as ceasefire talks failed on a fifth day of combat in Ukraine last night.
Anna Heraskina is a Ukrainian citizen living in the northeastern city of Kharkiv.
Along with her husband, Alexander Foster, of Auckland, she is in the process of applying for a partnership visa from INZ to move to New Zealand.
On Friday, she was told she needed to have her passport verified at the visa application centre in the capital Kyiv.
The invasion by Russian forces had begun a day earlier. Mr Foster’s mother, Dianne Souness, of Macandrew Bay, said she was astounded when she heard INZ’s request - it was "completely out of touch".
INZ should check on the situation on the ground before it insulted people’s intelligence, she said.
Her daughter-in-law, Mrs Heraskina, said on Monday there was an alert of a massive rocket attack by Russia.
Her friends were spending nights in bomb shelters, while she chose to stay at home to co-ordinate a team of translators.
She was "terrified" and had seen armed soldiers in her apartment building’s yard.
A line of tanks had passed a supermarket as people queued.
Members of her family were sheltering from Russian bombardments with children.
Neighbours had learnt to tell which direction rockets were travelling from by ear.
Mr Foster said the situation with INZ was "crazy"; there was a clear humanitarian reason to expedite visa applications for people in Ukraine.
Reuters reported Russian munitions killed 11 people and wounded dozens more in daylight strikes in Kharkiv on Monday.
Last night, INZ border and visa operations general manager Nicola Hogg said INZ’s thoughts were with the people of Ukraine, and apologised to the couple.
She said the government agency would turn off what was an automated response Ms Heraskina had received.
"This has been a fast-moving and dynamic situation, and we regret the distress this may have caused.
"We have communicated with Mrs Heraskina’s partner today to clarify the process and to assure them that the application will be processed as quickly as possible."
The visa processing centre in Kyiv was closed indefinitely,
and people in Ukraine were encouraged to apply online.
INZ was able to prioritise urgent visa applications from Ukrainian nationals, she said.
ImmiGreat Consultants licensed immigration adviser Stuart Scrimgeour said he was talking to INZ for the couple.
He described their situation as tragic and said he could not see how Mrs Heraskina would be able to apply for a visa online.
He had been "dumbstruck" when he was told by a senior INZ manager earlier that it was not expediting any visas from Ukraine.
"This is somebody whose life is potentially on the line."
