The situation at the centre in northern Paris threatens to reach crisis point over the next few days, Hidalgo said in a letter to Prime Minister Bruno Le Roux and Housing Minister Emmanuelle Cosse made public on Saturday.
The centre, opened in November, has 400 places for asylum-seekers, who are supposed to stay five to 10 days before being moved to centres elsewhere in France.
But over the last week the number of places available has been greatly reduced, Hidalgo writes, adding that the gap between supply and demand will soon be "untenable".
The centre, which was opened as street camps of migrants were cleared, is partly a victim of its own success.
Some 5,000 people - most of them Afghans or Sudanese - have passed through its doors since November.
Last Wednesday alone 150 people were taken in.
Fewer places in provinces
But some centres outside the capital were in holiday centres, which have had to revert to their original function during this fortnight's school holidays, and there has been an unexpected influx of migrants coming through Germany and Sweden with not all of them reaching the criteria for asylum.
Police sources also report tension between the Afghans and the Sudanese, according to Le Monde newspaper.
New street camps are starting to spring up and could become much bigger, Hidalgo says in her letter.
She calls on the government to provide more places, notably by opening a centre in Sarcelles, near Paris, on a site that she claims is "perfectly suited" to the task.