She is said to fear that Zimbabweans desperate to flee the cholera outbreak and Robert Mugabe’s regime, are buying false passports in neighbouring countries, where visas are not required for travel to Britain, before heading here.
Foreign Office sources are playing down her claim as "alarmist," leading to the potential for a serious rift within Whitehall.
Officials expressed concerns that the Home Office could use Miss Smith’s warnings about the potential arrival of thousands of refugees as an excuse to tighten border controls.
This could make it harder for legitimate asylum seekers escaping Mr Mugabe’s brutal police state to reach this country.
The BBC reported that the Zimbabwe was creating "real tension in Whitehall," as the Home Office is said to be calling for the introduction of visas for all countries in the region, a move opposed by the Foreign Office.
Miss Smith has told Cabinet colleagues that people fleeing Zimbabwe are buying false passports in countries such as South Africa and Botswana and using them to travel to the UK.
Mr Mugabe claims that the cholera outbreak in his troubled nation is over, but independent exerts confirm that at least 700 have died of the disease so far, and that the problem is spiralling. The British Red Cross has launched an emergency aid appeal.
Lord Malloch Brown, a Foreign Office Minister, said: "I think crisis is too strong a word for it. The Home Secretary has warned that we need to make sure we’ve got the appropriate arrangements in place to stop illegal papers being used to enter the country.
"She wants to make sure that her border agency is properly prepared for this. She briefed the Cabinet on that way, prior to a longer discussion on Zimbabwe."
There are already estimated to be 60,000 Zimbabweans living in Britain illegally, with another 12,000 seeking asylum including 8,000 who have been granted refuge status.