The prison population has reached record numbers following the recent rioting and lootingThe incident at Cookham Wood young offenders' institution in Kent on Saturday left two of them in hospital.
A Prison Service email urged governors in England and Wales to warn prisoners against revealing too much information, such as which gang they belonged to.
The prison population has reached a record 86,654 in the wake of the riots.
The memo said: "Over the past few days there has been emerging intelligence regarding the consequences of receiving public disorder remands/offenders.
"This is being assessed and processed with individual establishments responding appropriately. In due course this information will be shared more widely.
"A consideration that has been gathering pace is the safety of remands/offenders involved in the public disorder.
"This applies to the range of remands/offenders and is not limited to the young offender/young people estate but includes adult male and female offenders."
It continued: "There has been a nasty three person alleged assault. All three victims were public disorder remands, two currently in hospital.
"It is important that where remands/offenders are received thought is put into their background in terms of their experience of the custodial setting.
"Whilst the induction process ensures that remands/offenders are aware of the risks of stating where they live, what gang they may be in, what team they may support or faith they may be, it is worth ensuring that reception staff give a verbal brief and assess risk where you receive first time in custody people."
Prison Governors Association president Eoin McLennan-Murray told the BBC: "We've still got about 1,200 places and if they were then used up we get into the area of accommodation which we would rather keep free so we can operate well across the service.
"If we have to encroach into that area that gives us more spaces as well, but it becomes increasingly difficult if we get into the 'headroom', as we call it, because we need a certain number of places simply to operate the system."
Ministry of Justice (MoJ) figures showed that the prison population was rising at a rate of more than 100 people a day as the courts dealt with cases of rioting and looting.
Jail numbers increased by 723 over the past seven days from 85,931 last week, and 85,523 the week before. The MoJ said the "useable operational capacity" was 88,093.
The number of spare prison places is about 1,200 and there are also about 200 free spaces in immigration removal centres.
A Prison Service spokesman said: "We are managing an unprecedented situation and all the staff involved should be commended for their dedication and hard work during this difficult time.
"We currently have enough prison places for those being remanded and sentenced to custody as a result of public disorder.
"We are developing contingencies to increase useable capacity should further pressure be placed on the prison estate."
The service said these contingencies included introducing new facilities early and reopening mothballed accommodation.
The MoJ said 1,375 people had appeared before the courts on charges relating to the disturbances. The majority of these were for offences of burglary, theft and handling stolen property, and violence and violent disorder.
Some 62% of those charged have been remanded into custody. This compares to a remand rate of 10% for serious offences during 2010.
AnalysisLast year, Justice Secretary Ken Clarke hoped his prisons and sentencing Green Paper would cut the jail population by 3,000.
Now, prisons are fuller than ever. There's still some spare capacity - but officials are drawing up contingency plans for extra cells.
Magistrates have remanded almost 800 riot suspects - a six-fold increase in the usual numbers they lock up before trial. Many of those being remanded are first-time offenders who, at other times, would have been bailed.
Ken Clarke's original proposals included cutting remands by 1,300, reserving it only for those definitely going to jail. That would have saved prisons an estimated £50m.
As communities clean up and repair the damage, the hidden costs and challenges for prisons may grow as governors squeeze in hundreds of glum-faced looters, while trying to deliver reforms aimed at cutting reoffending.