Cambridge University risks damaging the quality of the student experience if it takes on many more undergraduates, Alison Richard, the vice-chancellor, has warned.
She also said it was vital for Cambridge to reduce its dependence on state funding to safeguard academic freedom.
Delivering her annual address to the university's Regent House, Professor Richard said Cambridge needed to "think hard" about the consequences of more growth in students as part of the Government's plans to expand higher education.
Ironically, the university is still seeking planning consent for its long-term aim of developing land to the north-west of Cambridge to build up to three new colleges.
But Professor Richard said that a significant rise in student numbers would gradually change the university's geography, staffing and "community structure" and could shift the balance between undergraduates and postgraduates. Growth, she added, also had the "potential to reshape the university's identity and its mission".
Professor Richard said: "In my view, significant overall expansion in student numbers (at Cambridge) at this time risks detracting from the quality of undergraduates' educational experience and from the quality of postgraduate students we are able to attract."
The university authorities have already asked academic departments and the colleges for their views about student numbers.
Student numbers at Cambridge have risen from a little over 11,000 to almost 18,000 in the past 30 years. In 1973-74, the university had 8,855 undergraduates and 2,513 postgraduates. By 2003-04, the numbers of undergraduates had increased to 11,751 and postgraduates to 5,967.
Responding to Professor Richard's speech, Charles Clarke, the Education Secretary, told The Times Higher: "There's a 'more means worse' debate that you can have, but I've never accepted that more does mean worse.
"What the vice-chancellor is saying is that these are questions we need to address. But there are also questions that we as a Government have to address about great universities, how we direct financial support and how we sustain their internationally competitive position. They are fair questions for her to put to us."
On finance, Professor Richard hinted in her speech that there would be a major college-based fundraising drive to coincide with the university's 800th anniversary celebrations in 2009.
"Like almost every top British university, Cambridge receives much more funding from the Government than from private sources for education as well as for research," she said.
"The safeguard of academic freedom makes it crucial for us to strive to reduce that state of dependence. There are several ways to achieve this. I will continue arguing publicly for the importance of academic freedom and will do my best to keep the debate alive and the issue engaged."
Last month, The Times Higher revealed that Cambridge's Board of Scrutiny - the university's internal watchdog - had warned that "tough decisions" about the range of academic work and future of courses were needed if it was to retain its world-class status and address a £71 million deficit.
The board suggested that the university should "face up to its financial constraints" and "prioritise core areas and those at which it excels".
Professor Richard said the university had to consider "whether Cambridge has adequate structures in place to attract the best overseas students and ensure that they benefit fully from the opportunities we offer... and explore the desirability of providing more overseas experiences for home students".