The confrontation comes days after Israeli troops stormed a Gaza-bound aid flotilla, leaving nine people dead and many injured.
That raid brought strong condemnation of Israel, especially from Turkey where most of the victims were from.
It is unclear whether Israeli forces have boarded the vessel or if they are just tracking from a distance.
The activists on board the Rachel Corrie had said that they would not resist.
The ship is named after a US college student who was crushed to death by an Israeli army bulldozer as she protested over house demolitions in Gaza.
Earlier, Israel told the ship to dock at the Israeli port of Ashdod and promised that the aid will be taken by road to Gaza.
The US urged the activists to do what the Israelis asked. However Irish Nobel peace laureate Mairead Maguire, who is aboard the ship, insisted it would not be diverted.
Activists said there were 20 people on board the Rachel Corrie, including five Irish nationals, six Malaysians and nine crew members.
The ship had been a part of the previous flotilla, but was delayed by technical problems.
The international outcry over Israel's actions when it intercepted the last flotilla has still not died down.
Accounts differ as to what happened when Israeli soldiers abseiled from helicopters on to the Turkish passenger ship Mavi Marmara in the early hours of last Monday.
Israel says their commandos were attacked with sticks and knives and used their weapons in self-defence. Activists say troops opened fire without provocation.