Hampshire have fined captain Dimitri Mascarenhas £1,000 following the comments he posted on Twitter on Sunday.
Mascarenhas has also apologised for his online outburst which was primarily aimed towards England national selector Geoff Miller.
Hampshire cricket chairman, Rod Bransgrove, said: "I met with Dimitri Mascarenhas and formally censured him, imposing a fine of £1,000. The fine has been set at this high level as I feel there is little point in imposing a ban, given the long-term nature of his injury.
"In coming to this conclusion I have taken into consideration Dimi's previous exemplary record. However, as club captain he understands that his actions carry more responsibility than others."
Mascarenhas added: "I realise that my actions were stupid and irresponsible and I regret any offence I may have caused.
"I apologise specifically to Geoff Miller who has always treated me fairly. I also apologise to Hampshire whom I feel I've let down. This was a silly, late-night conversation that got out of control and doesn't reflect my true views on Mr Miller.
"I've learnt a great deal about the dangers of social networking sites and encourage other players to think carefully before signing up to them."