Umpires Steve O'Shaughnessy and Martin Saggers twice inspected the sodden outfield with the hope of some action.
But, despite a dry afternoon, the pitch could not dry quickly enough and it was called off for the day at 16:00 BST.
Hampshire had earlier been rocked by the news that fast bowler Reece Topley had broken his hand batting.
The England World T20 fast bowler, who is making his debut in this match following his winter move from Essex, was struck on his right hand by Boyd Rankin early on making a career-best 15.
He is to see a specialist to check whether the injury is just a single or double fracture just below the knuckle.
On his 34th birthday, new Bears skipper Ian Bell is still hopeful of forcing a result given that Tuesday's weather forecast promises more dry spells.
Hampshire director of cricket Giles White told BBC Radio Solent:
"A little bit of time out the game isn't bad for us but we would like to be out there playing cricket as much as we can at this time of year.
"For us tomorrow we need to carry on batting and get what we can in terms of bonus points and bowl well. The game will take shape from there.
"It was a shame to lose a day today but the weather looks better tomorrow and we'll go again."
Warwickshire's hopes of building on their first-day domination were stymied by the Southampton weather as no play was possible on a rain-ruined day two.